agec 3413 test 1

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26) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by ________.

$1,333

122) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day?

$112

81) What is the maximum amount a manager would be willing to pay for one additional hour of machining time?

$1357.50 - $1350 = $7.50

106) Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

$175

25) The profit on the super product could increase by ________ without affecting the product mix.

$50

114) Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket?

$6.50

27) A change in the market has increased the profit on the super product by $5. Total profit will increase by ________.

$667

80) What is the shadow price for fabrication?

$7.50

53) In a graphical approach to a linear programming problem, the objective function is represented by a(n) ________.

(straight) line

52) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 As long as the slope of the objective function stays between ________ and ________, the current optimal solution point will remain optimal.

-5/3, -2/5

79) What is the shadow price for assembly?

32) If Taco Loco reduces the price of the X product by about 82 cents, then their optimal product mix will contain ________ X.

0 units (none)

84) How much space will be left unused? How many minutes of idle time remain for setting up the display?

0, 0

113) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the United States, and $3 for every performance outside the United States. Write an expression that could be used to compute the number of performances in order to cover the advance.

10000 = 2x + 3y

125) Ponder the following linear programming problem: Max Z = 5x1 + 6x2 Subject to: 3x1 + 4x2 ≤ 76 8x1 + 9x2 ≤ 123 3x1 + 3x2 ≤ 56 x1, x2 ≥ 0 What is the optimal solution point?

12.31 at x1 and 2.72 at x2 for an objective function value of 77.897

110) Aaron decides to rent out a spare bedroom on a part time basis for weary business travelers coming to his fair city. Aaron's bed-and-breakfast projects the following: Monthly fixed costs $2000 Variable cost per occupied room per night $10 Revenue per occupied room per night $165 How many nights would the room have to be occupied per month in order to break even?

12.90 nights

77) How many tractors and saws should be produced to maximize profit, and how much profit will they make?

15 tractors and 30 saws for $1350 in profit

123) The College Coffee Cafe buys tea from three suppliers. The price per pound is $15.00 from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budgeted $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions.

15.00 XA + 17.50 XB + 21 XC ≤ 175 XA + XB + XC ≥ 12 XC ≤ 4

108) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Write the expression for total revenue per month.

165x

78) Determine the sensitivity range for the profit for tractors.

20 ≤ x ≤ 60

23) The optimal number of regular products to produce is ________, and the optimal number of super products to produce is ________, for total profits of ________.

291.67, 133.33, $24,583

116) Administrators at a university will charge students $250 to attend freshman orientation. It costs $8,000 to reserve their grand ballroom, hire extra security, and bring in a moonwalk. Assume it costs $10 per student for the administrators to provide the course materials. How many students would have to register for orientation for the university to break even?

33.3

104) The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Price can vary between $10 and $50. How many units can be sold when the price is $10?

4750

123) Ponder the following linear programming problem: MIN Z = 3x1 + 8x2 Subject to: 3x1 + 4x2 ≥ 52 3x1 + 4x2 ≥ 38 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?

52 at x1 = 17.33 and x2 = 0.0

109) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 How many rooms would have to be occupied per month in order to break even?

64 rooms

30) Taco Loco will make the same quantity of X, Y, and Z if the amount of cheese at their disposal is between ________ pounds and ________ pounds.

74.67, 126

31) For humanitarian reasons, Taco Loco decides they would rather make product X than product Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to accomplish this reversal of demand is ________.

82 cents (81.8 cents)

121) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?

9.25 at x1 = 0 and x2 = 4.625

122) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?

9.25 at x1 = 0 and x2 = 4.625

(USE THIS FOR THE FOLLOWING QUESTIONS also refer to the graphs) The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 75) Which of the following is not a feasible schedule? A) two trips each to Pennsylvania and Wisconsin and one trip each to Florida, New York, and North Carolina B) four trips each to New York and North Carolina C) two trips each to Pennsylvania and North Carolina and one trip to Florida D) four trips to Wisconsin and five trips to New York

101) Which of these is a typical attribute of a decision support system? A) interactive B) intranet C) integrated D) insubordinate

105) The first step in solving a graphical linear programming model is to: A) plot the model constraints as equations on the graph and indicate the feasible solution area. B) plot the objective function and move this line out from the origin to locate the optimal solution point. C) solve simultaneous equations at each corner point to find the solution values at each point. D) determine which constraints are binding.

107) Multiple optimal solutions provide ________ flexibility to the decision maker. A) greater B) less C) greater or equal D) less or equal

36) For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: A) same product mix, different total profit. B) different product mix, same total profit as before. C) same product mix, same total profit. D) different product mix, different total profit.

41) Which of the following could not be a linear programming problem constraint? A) A + B ≤ -3 B) A - B ≤ -3 C) A - B ≤ 3 D) -A + B ≤ -3

42) Use the constraints given below and determine which of the following points is feasible. 14x + 6y ≤ 42 x - y ≤ 3 A) x = 1; y = 4 B) x = 2; y = 8 C) x = 2; y = 4 D) x = 3; y = 0.5

45) A shadow price reflects which of the following in a maximization problem? A) the marginal gain in the objective that would be realized by adding one unit of a resource B) the marginal gain in the objective that would be realized by subtracting one unit of a resource C) the marginal cost of adding additional resources D) the marginal gain of selling one more unit

52) Which additional resources would you recommend that Uncle Ulysses try to obtain? A) fabrication B) assembly C) paint D) crate

58) Variable cost: A) depends on the number of units produced. B) plus marginal cost equals fixed cost. C) is equal to total cost in deterministic models. D) is the same as average cost.

59) Which of the following could not be a linear programming problem constraint? A) 1A + 2B ≠ 3 B) 1A + 2B = 3 C) 1A + 2B ≤ 3 D) 1A + 2B ≥ 3

60) William's accountant made an error, and the budget has been reduced from $3000 to $2500. William's profit will go down by: A) $0. B) $1167. C) $350. D) $4667.

60) ________ are generally independent of the volume of units produced and sold. A) Fixed costs B) Variable costs C) Profits D) Average cost

64) At the break-even point: A) total revenue equals total cost. B) profit is maximized. C) revenue is maximized. D) costs are minimized.

65) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E + 30

65) If the price increases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales.

67) In the formulation of a ≥ constraint: A) a surplus variable is subtracted. B) a surplus variable is added. C) a slack variable is subtracted. D) a slack variable is added.

67) What should Captain Stubing's objective function be? A) Max Z = 1500 Bar + 5000 Food + 17000 Excursion B) Max Z = Bar + Food + Excursion C) Max Z = 900 Bar + 1500 Food + 5000 Excursion D) Max Z = 5 Excursions + 12 Cuisine + 7 Bar + 150000 Budget

68) If fixed costs decrease, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales.

68) Which of the following statements is not true? A) An infeasible solution violates all constraints. B) A feasible solution point does not have to lie on the boundary of the feasible solution. C) A feasible solution satisfies all constraints. D) An optimal solution satisfies all constraints.

71) Here's a portion of the sensitivity analysis for the constraints. Which of these statements is best? (refer to chart) A) If the budget rises to $150,001, then the optimal mix will result in an increased revenue of $3.40. B) If the excursions rise to 6, then the optimal mix will result in increased revenue of $19.24. C) If the restaurant constraint increased to 13, the optimal mix will result in increased revenues of $1,660. D) If the bar/food constraint rises to 1560, then the revenue will rise by a factor of 16.

74) How should the requirement that the bar setups should change at least every other day but no more than twice per day? A) 1 Bar ≥ 7; 1 Bar ≤ 28 B) 7 ≤ 1 Bar ≤ 28 C) 1 Bar ≤ 28 D) 1 Bar ≥ 7

76) The company with the highest variable cost is: A) A. B) B. C) C. D) D.

79) What is the maximum profit? A) $52,500 B) $48,000 C) $55,000 D) $56,250

80) In order to maximize profit, how many tables and how many chairs should be produced? A) T = 35, C = 0 B) T = 0, C = 48 C) T = 26.3, C = 32.8 D) T = 28.9, C = 30.7

81) Yowzah receives a frantic call from company C. Evidently the fixed cost they quoted was in rupees rather than dollars. If the current exchange rate is 60 rupees to the dollar, what is the net effect of an updated analysis? A) Company C is the bidder of choice throughout the range depicted in the graph. B) Company C has the highest total cost throughout the range depicted in the graph. C) Company C has the highest fixed cost of all four companies. D) Even beyond the range depicted in the graph, company C would be the bidder of choice.

86) Which line in Figure 1 is represented by the equation 2X + Y ≥ 8? A) BF B) CG C) DH D) AJ

87) Linear mathematical programming techniques assume that all parameters in the models are: A) known with certainty. B) unknown. C) predictable. D) unpredictable.

90) Line segment GH in Figure 2 represents the objective function. Which constraint has surplus? A) AB B) CD C) EF D) none of the constraints has surplus

91) Which of these techniques is typically considered part of the operations realm rather than the management science realm? A) forecasting B) queuing C) networks D) routing

92) What is the equation for constraint EF shown in Figure 2? A) 4X + 8Y ≥ 64 B) 4X + 8Y ≥ 12 C) 16X + 8Y ≥ 24 D) 16X + 8Y ≥ 32

92) Which one of the following management science methods is not a probabilistic technique? A) assignment models B) decision analysis C) queuing analysis D) statistical analysis

94) Consider the optimization problem represented by the graph in Figure 2. Line GH represents the objective function. Which of the following statements is best? A) This is a single optimal solution. B) All points along GH are optimal. C) All points on lines AB, CD and DE that touch the shaded region are optimal. D) All points in the shaded region are optimal

98) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario? A) Min Z = 1D + 0.5C B) Min Z = 2D + 1C C) Min Z = D + C ≤ 40 D) Min Z = D + C ≥ 3

98) Which of the following statements about infeasible problems is best? A) All of the possible solutions violate at least one constraint. B) All of the possible solutions violate all of the constraints. C) At least one of the possible solutions violates all of the constraints. D) At least one of the possible solutions violates at least one of the constraints.

Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $300 and for each table is $1500. 103) If the furniture company produces twenty tables and thirty-six chairs, which of the two resources will be completely used? A) labor only B) rich mahogany only C) both labor and rich mahogany D) neither labor and rich mahogany

114) Consider the following linear program: MIN Z = 50A + 60B s.t. 6A + 8B ≤ 300 14A + 7B ≥ 196 A ≥ 10 B ≥ 8 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. (graph)

A = 10, B = 8, Z = 980

121) What are some different types of decision support systems?

A DSS can be small and singular, such as an Excel spreadsheet set up for a single user to solve a specific type of problem. A DSS can also be large and complex, linking many users and databases. The DSS can be a data-oriented system or a model-oriented system. Some decision support systems (ERP systems) help managers make decisions about all facets of a company's operations.

45) ________ are at the endpoints of the constraint line segment that the objective function parallels.

Alternate optimal solutions

look at the table in the document 127) Formulate all elements of linear program to model your university effort. Include a narrative that explains each of the components.

Answers will vary, perhaps dramatically. A noble objective function would seek to maximize a GPA or minimize total cost. Constraints would likely include budget, hours in a day, financial capital, conflicts with social endeavors, and others.

95) Captain Stubing eyes the sensitivity report for his decision variables and Julie McCoy, Cruise Director, studies it. Her sneeze obscures part of the printout, leaving the captain scratching his bald head about the values of each of the three variables, Bar, Food and Excursion. Does he need all three? How would he know simply by reading the remaining legible portion of the report? refer to the chart

As luck would have it, we know that all three have positive values in the final solution. None of them shows as having a reduced cost, which means that they all must be in the solution.

101) A slack variable: A) is the amount by which the left side of a ≥= constraint is larger than the right side. B) is the amount by which the left side of a ≤= constraint is smaller than the right side. C) is the difference between the left and right side of a constraint. D) exists for each variable in a linear programming problem.

102) Instantaneous information about business transactions is achievable through the use of: A) point of sale systems and CPM B) point of sale systems and EDI C) decision support systems and EDI D) decision support systems and CPM

103) Which of these decision support systems is the most comprehensive with respect to an entire organization? A) an Excel spreadsheet B) an ERP C) QM for Windows D) OLAP

106) The optimal solution of a minimization problem is at the extreme point ________ the origin. A) farthest from B) closest to C) exactly at D) parallel to

109) If the feasible region for a linear programming problem is unbounded, then the solution to the corresponding linear programming problem is ________ unbounded. A) always B) sometimes C) never D) There is not enough information to complete this statement.

38) If the production manager decides to produce of 400 bottles of light beer and 0 bottles of dark beer, it will result in slack of: A) malt only. B) wheat only. C) both malt and wheat. D) neither malt nor wheat.

43) For the constraints given below, which point is in the feasible region of this minimization problem? 14x + 6y ≤ 42 x + 3y ≥ 6 A) x = 2; y = 5 B) x = 1; y = 2 C) x = 2; y = 1 D) x = 2; y = 3

45) The steps of the management science process are: A) problem definition, model construction, observation, model solution, implementation. B) observation, problem definition, model construction, model solution, implementation. C) model construction, problem definition, observation, model solution, implementation. D) observation, implementation, problem definition, model construction, model solution.

46) Given the following linear programming problem: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What would be the values of x and y that will maximize revenue? A) x = 5; y = 0 B) x = 0; y = 8 C) x = 0; y = 1 D) x = 1; y = 0

47) Given the following linear program that maximizes revenue: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What is the maximum revenue at the optimal solution? A) $120 B) $160 C) $185 D) $200

49) Which of the following is incorrect with respect to the use of models in decision making? A) They improve understanding of the problem. B) They promote subjectivity in decision making. C) They are generally easy to use. D) They provide a systematic approach to problem solving.

52) The limits of the problem and the degree to which it pervades other units in the organization must be included during the ________ step of the management science process. A) observation B) definition C) solution D) implementation

53) Suppose Uncle Ulysses is required by contract with the American Birding Association to make one birdhouse each week. How would this affect his profits? A) Profits would increase by $15. B) Profits would decrease by $17.15. C) Profits would increase by $0.00. D) Profits would decrease by $1E + 30.

55) The result of an effective decision-making process should be monitored in order to: A) reveal the break-even point. B) reveal errors in the implementation. C) keep fixed and variable costs distinct. D) change the scientific method.

57) Decision variables: A) measure the objective function. B) measure how much or how many items to produce, purchase, hire, etc. C) always exist for each constraint. D) measure the values of each constraint.

57) Uncle Ulysses is planning for next spring, and he is considering making only two products. Based on the results from the linear program, which two products would you recommend that he make? A) birdhouses and doghouses B) birdhouses and outhouses C) doghouses and outhouses D) He should continue to make all three.

60) Which of the following could be a linear programming objective function? A) Z = 1A + 2BC + 3D B) Z = 1A + 2B + 3C + 4D C) Z = 1A + 2B / C + 3D D) Z = 1A + 2B2 + 3D

61) William has decided that he can raise the price on the Curious t-shirt by 10% without losing sales. If he raises the price, his profits will: A) increase by $3. B) increase by $350. C) increase by $11.67. D) increase by $33.

62) Variable cost does not include: A) raw materials and resources. B) staff and management salaries. C) material handling and freight. D) direct labor and packaging.

63) What is the financial constraint? A) P+1.5W+2F+2Y+3C ≤ 250 B) 15P+20W+8F+25Y+22C ≤ 250 C) 15P+20W+8F+25Y+22C ≤ 80 D) 10P+15W+16F+2Y+18C ≤ 250

66) If the price decreases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales.

66) The region that satisfies all of the constraints in a graphical linear programming problem is called the: A) region of optimality. B) feasible solution space. C) region of non-negativity. D) optimal solution space.

68) What is the appropriate constraint for the budget? A) 1 Bar + 1 Food + 1 Excursion ≤ 150,000 B) 900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000 C) 1,500 Bar + 5,000 Food + 17,000 Excursion ≤ 150,000 D) 7 Bar + 12 Food + 5 Excursion ≤ 150,000

69) If fixed costs increase, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales.

72) Without satisfying the non-negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called: A) feasible. B) infeasible. C) semi-feasible. D) optimal.

73) Here's a lovely portion of the sensitivity report for the constraints. Which of these conclusions is reasonable? (refer to chart) A) Captain Stubing is scheduling more Excursions than he should be. B) Captain Stubing should exhaust his Budget. C) There is no Bar or Food being used. D) The value for Restaurant will rise by $1,660 for each additional cuisine required.

78) Which of these changes would have no effect on which supplier is chosen in the output range of 0 units to 20,000 units? A) Variable costs fall 10% for all bidders. B) Fixed costs rise 10% for all bidders. C) Companies A and B swap their figures for fixed costs. D) Companies C and D swap their figures for fixed costs.

79) Which level of anticipated demand is least sensitive to variations in fixed and variable cost estimates? A) 5,000 B) 10,000 C) 15,000 D) 20,000

82) Consider the following maximization problem. MAX z = x + 2y s.t. 2x + 3y ≤ 6 5x + 6y ≤ 30 y ≥ 1 The optimal solution: A) occurs where x = 4.67 and y = 1.11. B) occurs where x = 0 and y = 2. C) occurs where x = 6 and y = 0. D) results in an objective function value of 12.

82) Which of the following statements is false? A) Decision models selectively describe the managerial situation. B) Decision models consider all factors from the real world. C) Decision models designate performance measures that reflect objectives. D) Decision models designate decision variables.

88) Decision analysis is a ________ technique. A) linear mathematical programming B) probabilistic C) network D) non-linear programming technique

88) In Figure 1, the constraint AJ: A) is a binding constraint. B) has no surplus. C) does not contain feasible points. D) contains the optimal solution.

95) In order for an optimization problem to have multiple optimal solutions: A) the objective function and one constraint must have the same y-intercept. B) the objective function and one constraint must have the same slope. C) two or more of the constraints must not have intersection points. D) two or more of the constraints must have the same slope.

97) How would multiple optimal solutions typically appear on a graphical solution? A) a point B) a line C) a plane D) a cube

97) Larry's Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is: A) 5S + 3.5W ≤ 160. B) Min 5S + 3.5 W. C) Max 5S + 3.5 W. D) Min 5S + 3.5W ≥ 160.

Figure 1: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. (refer to the figure) 83) This linear programming problem shown in Figure 1 is a(n): A) maximization problem. B) minimization problem. C) irregular problem. D) cannot tell from the information given

Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $300 and for each table is $1500. (use this to refer to the following and graph) 78) Which of the following is not a feasible production plan? A) 35 chairs and 20 tables B) 20 chairs and 35 tables C) 25 chairs and 30 tables D) 30 chairs and 25 tables

The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 102) The campaign manager elects to take one trip each of Pennsylvania, Florida and North Carolina, two trips to Wisconsin, and three trips to New York. Which resources will be completely used? A) only money B) only time C) time and money D) neither time nor money

30) ________ is the term used to describe a collection of numbers that is massive in size.

Big data

31) ________ uses large amounts of data with management science techniques and modeling to help managers make decisions.

Business analytics

108) Which of the following special cases does not require reformulation of the problem in order to obtain a solution? A) unboundedness B) infeasibility C) alternate optimality D) Each one of these cases requires reformulation.

40) What is the optimal weekly profit for the scenario in Table 3.3? A) $1000 B) $900 C) $800 D) $700

44) What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y 2x + 4y ≥ 12 5x + 2y ≥ 10 A) x = 0; y = 3 B) x = 0; y = 5 C) x = 5; y = 0 D) x = 6; y = 0

47) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? A) a decision variable B) an objective function C) a constraint D) a parameter

48) For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________. A) decrease, resource B) increase, parameter C) improvement, resource D) decrease, parameter

48) There is considerable overlap in the scientific method and management science techniques. Which of the following steps is shared between them? A) observation B) problem definition C) model construction D) implementation

49) Sensitivity analysis is the analysis of the effect of ________ changes on the ________. A) price, company B) cost, production C) parameter, optimal solution D) constraint, parameter

50) For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint: A) will have a positive value. B) will have a negative value. C) will have a value of zero. D) could have a positive, negative or a value of zero. (no sign restrictions).

50) The field of management science: A) approaches decision making irrationally with techniques based on the scientific method. B) is another name for management or human resources management. C) concentrates on the use of quantitative methods to assist managers in decision making. D) is completely separate and distinct from all other disciplines.

51) For a resource constraint, either its slack value must be ________ or its shadow price must be ________. A) negative, negative B) negative, zero C) zero, zero D) zero, negative

51) The processes of problem observation: A) cannot be done until alternatives are proposed. B) requires consideration of multiple criteria. C) is the first step of decision making. D) is the final step of problem solving.

53) ________ involves determining the functional relationship between variables, parameters, and equations. A) Problem observation B) Problem definition C) Model construction D) Model solution

54) Uncle Ulysses feels that his prices are too low, particularly for his birdhouses. How much would he have to charge for his birdhouses before it is profitable for him to make and sell them? A) $15.00 B) $17.15 C) $32.15 D) $47.15

54) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision? A) model implementation B) problem definition C) model solution D) problem formulation

57) The indicator that results in total revenues being equal to total cost is called the: A) marginal cost. B) marginal volume. C) break-even point. D) profit mix.

58) In a linear programming problem, a valid objective function can be represented as: A) Max Z = 5xy B) Max Z 5x2 + 2y2 C) Max 3x + 3y + 1/3 z D) Min (x1 + x2) / x3

59) If one of William's machines breaks down, it usually results in about 15 minutes of downtime. When this happens, Billy's profits are reduced by: A) $250. B) $180. C) $150. D) $350.

59) The components of break-even analysis are: A) cost and profit. B) volume and cost. C) volume, cost and profit. D) volume and profit.

62) The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should: A) refuse to buy any cheese. B) buy less than 80 pounds of cheese for $1.45 per pound. C) buy 46 pounds or less of cheese for $1.45 or less. D) buy at least 126 pounds of cheese for $5.33 or less.

62) What is the time constraint? A) P+1.5W+2F+2Y+3C ≤ 250 B) P+1.5W+2F+2Y+3C ≤ 80 C) 10P+15W+16F+2Y+18C ≤ 80 D) 15P+20W+8F+25Y+22C ≤ 80

63) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81.

63) Which variable is not a component of break-even analysis? A) fixed costs B) variable costs C) number of employees D) number of customers

64) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds

65) The ________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant. A) additive B) divisibility C) certainty D) proportionality

66) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00 D) $158.18

67) The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters A) graphical solution B) decision analysis C) sensitivity analysis D) break-even analysis

69) A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost niched product while meeting the dietary guidelines for protein and sodium. Once the model has been run, the surplus variable in the sodium constraint has a value of 1300 milligrams. The best interpretation of this outcome is: A) the value of the sodium in a hot dog is 1300. B) the amount of sodium in a single hot dog should be 1300 milligrams. C) the minimum cost hot dog has 1300 milligrams more sodium than required. D) a hot dog should have at least 1300 milligrams of sodium.

69) What is the appropriate constraint for the requirement that there should be at least one different bar setup for every different type of food? A) Bar - Food ≤ 0 B) Bar + Food ≤ 0 C) Food - Bar ≤ 0 D) Food + Bar ≥ 0

70) Which of these statements is best? A) An unbounded problem is also infeasible. B) An infeasible problem is also unbounded. C) An unbounded problem has feasible solutions. D) An infeasible problem has unbounded solutions.

71) A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $120 B) $150 C) $175 D) $200

72) A university is planning an online seminar. It costs $30 to live stream an instructor from Elbonia. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $55 B) $15 C) $26.50 D) $75.75

74) It costs $6,000 to start a production process. Variable cost is $2 per unit and revenue is $5 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units

74) Which of the following is not a typical characteristic of a linear programming problem? A) Restrictions exist. B) A choice among alternatives is required. C) The problem can be solved graphically. D) The problem has an objective.

77) Over the range of demand shown by this graph, which action would completely remove one of the potential suppliers from consideration? A) lowering A's fixed cost by 10% B) raising B's variable cost by 10% C) raising C's variable and fixed costs by 10% D) lowering D's fixed cost by 25%

77) ________ is used to analyze changes in model parameters. A) Optimal solution B) Feasible solution C) Sensitivity analysis D) A slack variable

80) Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the two bidders? A) 3,250 B) 3,500 C) 3,750 D) 4,000

84) The equation for constraint DH as shown in Figure 1 is: A) 4X + 8Y ≥ 32. B) 8X + 4Y ≥ 32. C) X + 2Y ≥ 8. D) 2X + Y ≥ 8.

85) A technique that assumes certainty in its solution is referred to as: A) stochastic. B) probabilistic. C) deterministic. D) parametric.

87) Which of the following constraints shown in Figure 1 has a surplus greater than 0? A) BF B) CG C) DH D) AJ

89) Which one of the following techniques is not a mathematical programming technique? A) linear programming models B) transportation models C) analytical hierarchy process D) integer linear programming technique

90) The analytical hierarchy process is used to: A) convert qualitative problems into quantitative problems B) minimize the number of levels in an organization C) choose among several alternatives D) determine the optimal route between two points

93) Consider the optimization problem represented by the graph in Figure 2. The objective function is represented by line GH. Where is the optimal solution? A) the intersection of lines AB and EF B) the intersection of lines AB and CD C) the intersection of lines CD and EF D) the upper right corner of the shaded region

94) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. At most, the baker could make: A) 4 batches of bread. B) 2 pounds of muffins. C) 8 batches of cookies. D) 24 pounds of flour.

96) An objective function: A) shows where the break-even point is. B) describes how much of a resource can be used. C) can represent costs or profits. D) describes something to be maximized.

99) Greg, a young entrepreneur, has developed an aggressive business plan and is presenting his profit projections on the popular show Shark Tank in hopes of securing some venture capital. He concludes his presentation with an LP model of his planned product mix, and is convinced he will seal the deal by demonstrating that his profits are limitless since his LP model is unbounded. What should the sharks tell him? A) "Limitless profits sound fantastic, here's a blank check." B) "Limitless profits are possible only in minimization models, and we want you to maximize profits." C) "Unlimited profits aren't possible. You must have made a mistake in your LP model." D) "Limitless profits are possible only in maximization models, and we want you to minimize profits."

99) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario? A) 7C + 4D ≥ 3 B) 1C + 2D ≤ 40 C) .5C + 1D ≤ 40 D) 7C + 4D ≥ 1.5

A) None of items Two, Three or Four is being used. B) Adding two units of One will increase the objective function value by two. C) Taking away four units of One will lower the objective function value by four. D) The most valuable resource is Four.

Figure 2 ( refer to the figure) 89) Consider the optimization problem represented by the graph in Figure 2. Which of the following statements is best? A) This is a maximization problem with a feasible solution. B) This is a maximization problem with no feasible solution. C) This is a minimization problem with a feasible solution. D) This is a minimization problem with no feasible solution.

107) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Write the expression for total cost per month.

C(x) = 8000 9 40x

127) What is the point of indifference between company A and company C? How does this point of indifference affect Yowzah's decision?

Company A appears to have a fixed cost of 75,000 and company C appears to have a fixed cost of 160,000. The variable cost (slope) for company A is (375,000 - 75,000)/20,000 = 15. The variable cost (slope) for company C is (280,000 - 160,000)/20,000 = 6. The point of indifference can be found by setting the two lines equal to each other, so 75,000 + 15x = 160,000 + 6x; 9x = 85,000; x = 9444.4 The point of indifference doesn't affect Yowzah's decision in this range as both companies have higher costs than their fierce rival company B around this range of output.

99) Interpret this sensitivity report for the constraints. refer to the chart

Constraint One is the only binding constraint; it has a shadow price of 1, meaning that if the RHS increased by 1, the optimal value of the objective function would rise by 1. This works in the very limited range up to 46.6666667. If the RHS dropped by 1, the objective function value would drop by 1 all the way down to a RHS equal to 0. The other constraints have slack; if constraint Two's RHS drops by 2 or more, the optimal answer would change. Constraint Four would become binding if the RHS was 72 or lower and constraint Three enters the picture if the RHS drops to 27 or lower. For the moment, any increase in the RHS for Two, Three or Four would have no impact on the optimal answer.

100) Marriott used which of the following management science techniques to help improve profit by $120 million over two years? A) optimization, decision analysis, and forecasting B) forecasting, queuing theory, and inventory analysis C) queuing theory, optimization, and inventory analysis D) forecasting, simulation, and optimization

100) Multiple optimal solutions can occur when the objective function is ________ a constraint line. A) unequal to B) equal to C) perpendicular to D) parallel to

104) Consider the following linear program: MAX z = 5x + 3y s.t. x - y ≤ 6 x ≤ 1 The optimal solution: A) is infeasible. B) occurs where x = 1 and y = 0. C) occurs where x = 0 and y = 1. D) results in an objective function value of 5.

37) A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in: A) the same product mix, different total profit. B) a different product mix, same total profit as before. C) the same product mix, same total profit. D) a different product mix, different total profit.

39) Which of the following is not a feasible solution for the scenario in Table 3.3? A) 0 L and 0 D B) 0 L and 400 D C) 200 L and 300 D D) 300 L and 200 D

46) A model is a functional relationship that includes: A) variables. B) parameters. C) equations. D) all of the above

55) Uncle Ulysses' available hours for crating have fallen from 20 hours to 15 hours because of a new "one-hour nap time" rule for this five-year-old worker. How will this affect his profits? A) Profits will increase by $7.69. B) Profits will decrease by $7.69. C) Profits will decrease by $12.31. D) Profits will not change.

56) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 Which of these objective functions will lead to the same optimal solution? A) 2x1 + 1x2 B) 7x1 + 8x2 C) 80x1 + 60x2 D) 25x1 + 15x2

56) Uncle Ulysses can obtain an additional 10 hours of painting capacity free of charge by training his helper monkey to paint. If he did this, how would his profits be affected? A) Profit would increase by $6.92. B) Profits would decrease by $20. C) Profits would increase by $1.58. D) Cannot tell from the information provided.

56) Which of these disciplines typically does not fall under the umbrella of analytics? A) information systems B) statistics C) management science D) operations management

58) If William could acquire more of any resource, which would it be? A) adding resources cannot improve his profit B) money C) tie-dying labor D) machining time

61) The purpose of break-even analysis is to determine the number of units of a product to sell that will: A) appeal to the consumer. B) result in a profit. C) result in a loss. D) result in zero profit.

64) The ________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant. A) additive B) divisibility C) certainty D) proportionality

70) Administrators at a university will charge students $175 to attend freshman orientation. It costs $10,000 to reserve a room, hire extra security, and bring in a moonwalk. Assume it costs $15 per student for the administrators to provide the course materials. How many students would have to register for orientation for the university to break even?A) 54.25 B) 58 C) 56 D) 62.5

70) Here's the sensitivity report for the decision variables. Which of these conclusions is correct? (refer to the chart for this) A) If the cost of the Bar variable is reduced by more than 0, then more of it will be used. B) If the cost of the Bar variable is increased by more than 0, then more of it will be used. C) If the coefficient for the Cuisine variable rises to 1660, then more of it will be used. D) It doesn't matter how much money they make on excursions; the optimal answer will continue to be 24.24 of them.

71) The optimal solution to a linear programming model that has been solved using the graphical approach: A) is typically located at the origin. B) must be below and on the left side of all constraint lines. C) must be above and the right of all constraint lines. D) is typically at some corner of the feasible region.

72) Based on the variable cells sensitivity report, what conclusion is best? (refer to chart) A) The value of Excursion can be infinite, since 1E + 30 is 10 to the 30th power. B) The values of Bar, Cuisine, and Excursion are all equal to zero. C) The values of Bar and Cuisine can be negative since they have allowable decreases of 1E + 30. D) The optimal value for the objective function is $490,080

73) An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: Max 2T + 3S + 4ST s.t 3T + 6S ≤ 40 10T + 10S ≤ 66 10T + 15S ≤ 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models? A) divisibility B) proportionality C) certainty D) additivity

73) It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units

75) The company with the lowest variable cost is: A) A. B) B. C) C. D) D.

76) What is the total percentage increase if the candidate makes the following schedule? A) 10% B) 11% C) 12% D) 13%

81) The theoretical limit on the number of constraints that can be handled by a linear programming problem is: A) 2. B) 3. C) 4. D) unlimited.

83) Decision support systems and sensitivity analysis are useful management science tools for answering the question: A) by when? B) who else? C) how much? D) what if?

84) A difficult aspect of using spreadsheets to solve management science problems is: A) obtaining the solution to standard management science problems. B) data entry. C) performing sensitivity analysis. D) setting up a spreadsheet with complex models and formulas.

85) Which of the following points is not feasible for the graph shown in Figure 1? A) A B) B C) H D) G

86) Classification of management science techniques does not recognize: A) linear mathematical programming. B) probabilistic techniques. C) network techniques. D) computer programming.

91) What is the equation for the constraint AB shown in Figure 2? A) 3X + 12Y ≥ 15 B) X + 4Y ≥ 12 C) X + Y ≥ 15 D) 12X + 3Y ≥ 36

93) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is: A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8. B) x1 + x2 + x3 ≥ 24. C) x1 + x2 + x3 ≤ 24. D) 4x1 + 3x2 + 2x3 ≤ 24.

96) An optimization problem that has multiple optimal solutions: A) means that there are actually no optimal solutions. B) is reflected by the entire feasible region being optimal C) means that the surplus for a third constraint cannot be calculated. D) provides the decision-maker with increased flexibility.

A) Item A can drop in value all the way down to 1.25 before it harms the result. B) Items B and C are the only elements in the final model. C) The final value of this problem is 9. D) Insisting that one additional unit of B, be included in the model will reduce the profit by $2.

The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 61) What is the objective function? A) MIN 10P+15W+16F+2Y+18C B) MAX 10P+15W+16F+2Y+18C C) MIN 15P+20W+8F+25Y+22C D) MAX P+1.5W+2F+2Y+3C

28) ________ are pieces of information from the problem environment.

Data

98) Interpret this sensitivity report for the variable cells.

Decision variable A is the only variable that appears in the optimal answer. Nine units of A are optimal and the coefficient is 5, so the objective function value is 45. The optimal answer will remain nine units of A as long as the coefficient remains in the range of 3.75 to infinity. Decision variable B, with a coefficient of 6, is not used in the optimal answer. If the coefficient of B increased to 8 or beyond, it would enter the model with a positive value. If the value of B's coefficient drops by any amount, it will not enter the decision space. Similarly, C with an objective coefficient of 1, is not in the answer unless the coefficient increases to 3 or beyond. If we added a constraint that required either B or C to enter the solution, the value of the objective function would drop by 2, from 45 to 43.

33) ________ are mathematical symbols representing levels of activity.

Decision variables

115) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. (refer to graph) If this is a maximization, which extreme point is the optimal solution? (graph)

44) ________ systems connect the business functions of an entire company.

Enterprise resource planning, ERP

11) Management science modeling techniques provide results that are known with certainty.

FALSE

11) The equation 8xy = 32 satisfies the proportionality property of linear programming.

FALSE

11) The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change.

FALSE

12) Typically, finding a corner point for the feasible region involves solving a set of three simultaneous equations.

FALSE

13) Objective functions in linear programs always minimize costs.

FALSE

14) Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once.

FALSE

15) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded.

FALSE

15) There is exactly one optimal solution point to a linear program.

FALSE

16) In general, an increase in price increases the break-even point if all costs are held constant.

FALSE

16) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20.

FALSE

17) If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease.

FALSE

17) The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin.

FALSE

17) To determine the change in the objective function for any increase in right-hand side, simply multiple the shadow price by the increase in the right-hand side.

FALSE

18) A minimization model of a linear program contains only surplus variables.

FALSE

19) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem.

FALSE

2) A variable is a value that is usually a coefficient of a parameter in an equation

FALSE

2) When the right-hand sides of two constraints are both increased by one unit, the value of the objective function will be adjusted by the sum of the constraints' prices.

FALSE

20) Slack variables are only associated with maximization problems.

FALSE

21) A typical objective function might be written as 3S + 2R + 5Z ≤ 20.

FALSE

21) Surplus variables are only associated with minimization problems.

FALSE

22) If the objective function is parallel to a constraint, the constraint is infeasible.

FALSE

23) In both an objective function and a constraint, the decision variables are represented by numbers.

FALSE

23) Multiple optimal solutions occur when constraints are parallel to each other.

FALSE

24) A DSS is a type of ERP system.

FALSE

25) The first step in formulating a linear programming model is to define the objective function.

FALSE

28) Linear programming problems can model decreasing marginal returns.

FALSE

3) Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3.

FALSE

31) In the absence of nonnegativity constraints, our solution cannot have zero values for decision variables.

FALSE

32) If there are no feasible solutions to a linear programming model, then the best course of action for a manager is to choose a solution that violates at least one constraint.

FALSE

4) Sensitivity ranges can be computed only for the right-hand sides of constraints.

FALSE

5) Proportionality means the slope of a constraint is proportional to the slope of the objective function.

FALSE

7) The first step of the management science process is to define the problem.

FALSE

7) The terms in the objective function or constraints are multiplicative.

FALSE

8) The sensitivity range for an objective function coefficient is the range of values over which the profit does not change.

FALSE

8) The term big data refers to numbers of large magnitude, i.e., greater than or equal to one billion.

FALSE

35) ________ costs are independent of the volume of goods produced and remain constant.

Fixed

115) A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs $20,000 to rent and the smaller of which costs $12,000 to rent. Ticket prices for the smaller venue are $20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue?

Increase 40%

117) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. Provide a full description of the type of constraint is represented by line JK. (graph)

Line JK is a nonbinding, greater than or equal constraint. It cannot be a less than or equal constraint because then the problem would be infeasible.

131) A company producing a standard line and a deluxe line of fidget spinners has the following time requirements (in minutes) in departments where either model can be processed. Standard Deluxe Stamping 0.3 0.4 Extruding 0.25 0.5 Fidget Testing 1 1.5 (number above come from a chart in document) The standard models contribute $2 each and the deluxe $3 each to profits. Because the company produces other items that share resources used to make the fidget spinners, the stamping machine is available only 15 minutes per hour, on average. The extruding unit has 20 minutes available each hour. There are two ADHD certified inspectors for fidget testing, but their availability is only 45 minutes per hour because they're easily distracted. Let S = number of standard fidget spinners produced per hour D = number of deluxe fidget spinners produced per hour Write the formulation for this linear program and solve it using the graphical method. (refer to the graph as well)

Max $2S + $3D s.t 0.3S + 0.4D ≤ 15 0.25S + 0.5D ≤ 20 1S + 1.5D ≤ 45 The optimal product mix is to make 30 Deluxe units and no Standard units.

124) The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend. Develop an objective that maximizes profit.

Max 1.25x1 + 1.40x2 + 1.50x3

124) The international man of mystery knew the finest haberdashers the world over and constantly sought to expand his dazzling array of fine suits, ties, and cufflinks. Closet space was at a premium however, so purchases were carefully weighed. Each suit provides 23 units of dazzlement, each tie 14, and a set of cufflinks is worth an easy 8. A suit takes up 0.5 cubic feet of closet space and $900 of budget. A tie costs $135 and cufflinks cost $100 per set. Cufflinks are tiny - even in the original box, they take up only .01 cubic feet while ties occupy a lusty .25 cubic feet. He has budgeted $12,000 for clothes on this trip and has 20 cubic feet of closet space left to fill. Formulate an objective function and constraints to model this situation.

Max Dazzlement = 23S + 14T + 8C subject to: 900S + 135T + 100C ≤ 12,000 0.5S + 0.25T + 0.01C ≤ 20

(refer to this in the notes) 91) What are the appropriate objective function and constraints for this scenario?

Max Z = 1500B + 5000C + 17000E subject to: 900B + 1500C + 5000E ≤ 150,000 E ≥ 5 C ≥ 12 B ≥ 7 B ≤ 28 C - B ≤ 0

118) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost.

Min 6x1 + 5.5x2

120) The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation.

Min Z = $4005C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0

130) Consider the following linear programming problem: MIN Z = 2x1 + 3x2 Subject to: x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 + 6x2 ≤ 60 x1, x2 ≥ 0 What is the optimal solution?

Multiple optimal solutions exist between the extreme point (0,10) and (6.92,5.38) along the line with a slope of -2/3.

40) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques.

Networks

129) Given this set of constraints, for what objective function is the point x = 5, y = 3 in the feasible region? s.t 3x + 6y ≤ 30 10x + 10y ≤ 60 10x + 15y ≤ 90

No objective function can move that point into the feasible region.

34) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic.

Probabilistic

126) List the four properties of linear programming models and provide an example of a violation of each.

Properties and brief discussions are contained in the table. Counter examples will vary.

87) You are offered the chance to obtain more space. The offer is for 10 units and the total price is $1000. What should you do? Why?

Reject the offer because the $100 per unit cost exceeds the shadow price of $80.

20) ________ is the analysis of the effect of parameter changes on the optimal solution.

Sensitivity analysis

So, 6 minutes of studying and 3 minutes of working on assignments was all that was required for my first born to successfully complete his first semester with something other than a 0.0 GPA. Sad, but true. 113) Consider the following linear program: MAX Z = 25A + 30B s.t. 12A + 15B ≤ 300 8A + 7B ≤ 168 10A + 14B ≤ 280 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Solution shown below. A = 11.67, B = 10.67

42) ________ is the difference between the left- and right-hand sides of a greater than or equal to constraint.

Surplus

1) A management science solution can be either a recommended decision or information that helps a manager make a decision.

TRUE

1) Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints.

TRUE

1) The shadow price for a positive decision variable is 0.

TRUE

10) Business analytics brings together the disciplines of information systems, management science, statistics, and mathematical modeling.

TRUE

10) If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.

TRUE

10) Linear programming models exhibit linearity among all constraint relationships and the objective function.

TRUE

12) Sensitivity analysis allows the modeler to relax the certainty assumption.

TRUE

12) The term sensitivity analysis refers to testing how a problem solution reacts to changes in one or more of the model parameters.

TRUE

13) The terms "shadow price" and "dual price" mean the same thing.

TRUE

13) Variable costs depend on the number of items produced.

TRUE

14) Fixed cost is the difference between total cost and total variable cost.

TRUE

14) The feasible solution area contains infinite solutions to the linear program.

TRUE

15) The break-even point is the volume that equates total revenue with total cost.

TRUE

16) One type of sensitivity analysis is to add a new constraint to the model.

TRUE

18) Managers utilize spreadsheets to conduct their own analyses in management science studies.

TRUE

18) The Allowable Increase for Calimari in the sensitivity report was 25 with a final value of 13, a shadow price of $16, and an objective coefficient of 10. Luigi added 5 units of Calimari and increased his profit by $80.

TRUE

19) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point.

TRUE

2) The objective function always consists of either maximizing or minimizing some value.

TRUE

20) Management science modeling techniques focus on model construction and problem solution.

TRUE

22) Decision Support Systems (DSS) use computers to help decision makers address complex problems.

TRUE

24) Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

TRUE

25) A key element of a decision support system (DSS) is the person using the system.

TRUE

26) A linear programming problem requires a choice between alternative courses of action.

TRUE

26) An ERP system is software that is capable of connecting functions and processes across an entire company.

TRUE

27) A company may use an intranet for communication among its own business units that are scattered geographically.

TRUE

27) The term continuous is synonymous with divisible in the context of linear programming.

TRUE

29) One of the most frequent objectives of business forms is to gain the most profit possible.

TRUE

3) Parameters are known, constant values that are usually coefficients of variables in equations.

TRUE

3) The objective function is a linear relationship reflecting the objective of an operation.

TRUE

30) We have George Dantzig to thank for developing linear programming.

TRUE

4) Both objective functions and constraints contain parameters.

TRUE

4) Data are pieces of information from the problem environment.

TRUE

5) A model is a mathematical representation of a problem situation including variables, parameters, and equations.

TRUE

5) The marginal value of any scarce resource is the dollar amount one should be willing to pay for one additional unit of that scarce resource.

TRUE

6) A management science technique usually applies to a specific model type.

TRUE

6) Sensitivity analysis determines how a change in a parameter affects the optimal solution.

TRUE

6) The terms in the objective function or constraints are additive.

TRUE

7) The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

TRUE

8) All linear programming models exhibit a set of constraints.

TRUE

9) A key component of business analytics is the recent availability of large amounts of data.

TRUE

9) The sensitivity range for a constraint quantity value is the range over which the shadow price is valid.

TRUE

9) When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn.

TRUE

97) Provide an interpretation of the Budget, Excursions constraints portion of the Ranging report for Captain Stubing.

The Restaurant constraint has a dual value of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3,320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no dual value - it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day.

93) Captain Stubing runs the LP model associated with the scenario and reads the following about the constraints in the Excel sensitivity report. Gopher is unable to provide an interpretation, but you volunteer to provide insight on the Restaurant and Excursions portion of the sensitivity report. refer to the chart

The Restaurant constraint has a shadow price of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no shadow price — it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day

105) A production process requires a fixed cost of $50,000 and the variable cost per unit is $25. The revenue per unit was projected to be $45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break-even point?

The break-even point will be higher, at 3424 units, which is a 37% increase.

112) A business analyst describes his company's profit function as 3x2 + 6x - 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost?

The fixed cost is $200, but we can't determine exactly what the price and variable cost are.

119) Given this model Maximize Z = 6S + 4A subject to: 12S + 10A ≥ 100 6S + 8A ≥ 64 7S - 3A ≥ 36 What is the optimal solution and the surplus associated with the first constraint?

The optimal solution lies at S = 6.48 and A = 3.13. The s1 variable is 9.1892

111) A novice business analyst develops the following model to determine the optimal combination of socks and underwear to take on his next business trip. The model is as follows: (refer to the graph) Maximize 5S + 7U subject to: 3S - 2U ≤ 45 7S + 3U ≤ 33 2S + 8U ≤ 70 Solve this problem graphically and determine how many of each item the analyst should pack.

The optimal solution lies at the point representing 1.08 socks and 8.48 underwear. I suppose this is why I referred to the analyst as a novice.

116) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. (refer to graph) What are the equations for any two greater than or equal constraints for this problem? (graph)

The three greater than or equal constraints are A≥10, B≥8, 14A+7B≥98

Corner points and the objective function value in (Socks,Underwear) order are: Z(0,0) = 0 Z(4.714,0) = 23.57 Z(0,8.75) = 61.25 Z(1.08. 8.48) = 64.76 optimal 112) Nathan enters the final exam period needing to pull off a miracle to pass his three toughest classes, Healthy Life Choices, Success Central, and Walking Fitness. Naturally he would also prefer to expend as little effort as possible doing so and as luck would have it, he knows a guy that can help optimize his time and GPA using the magic of management science. The model they develop is built around the notion of time spent studying and doing all the assignments he has neglected throughout the semester. The model is as follows, where S represents time spent studying (in minutes) and A represents time spent making up assignments (also in minutes). Maximize Z = 6S + 4A subject to: HLC 12S + 10A ≥ 100 SC 6S + 8A ≥ 64 W 7S - 3A ≥ 36 Graphing was never one of Nathan's strengths, so it is up to you to develop a graphical solution to his problem and advise him on how much time should be invested in studying and how much time should be spent catching up on assignments. (refer to the graph)

The two corner points meriting investigation are (in (Studying, Assignments) order) Z(10.67,0) = 64 Z(6.48,3.13) = 51.46 the optimal solution

126) Which of the companies has the greatest variable cost?

The variable cost is reflected by the slope, and the line representing company A starts lower than the others on the left side of the graph and ends higher than all others, thus it must have the greatest slope and therefore highest variable cost.

Yowzah Bids Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. René Descartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting. 125) Describe a general approach for determining the variable cost of any of the companies in this plot.

The variable cost is reflected by the slope, so a rise over run formulation can be used. The leftmost edge of the graph represents x = 0 and the rightmost is a value of 20,000, which is a difference of 20,000. By subtracting the leftmost y-coordinate from each line from the rightmost, the rise can be computed. Then dividing the rise, or ∆y, by the run, ∆x, to determine the variable cost.

92) Captain Stubing runs the LP model associated with the scenario and reads the following about the variable cells in the Excel sensitivity report. Provide an interpretation. refer to chart

There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an allowable increase of $1,560, so if the profit on a bar setup increased by that amount over the current value, i.e., all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change).

96) Provide an interpretation of the Ranging Report from QM

There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an upper bound of $3,060, so if the bar profit increases all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change).

94) Using just the Constraints portion of the sensitivity report, indicate which of Captain Stubing's limitations are reducing his profit. refer to the chart

Three of the constraints have shadow prices of zero, meaning they are non-binding and thus do not limit his profit. The Bar/Food combination, that is the requirement that there should be at least one bar type for each cuisine type, is holding him back. The budget constraint also limits the profit, for each additional budget dollar he had to start the cruise, he could generate an additional $3.40. If the right hand side of these constraints were increased, then additional profit could be earned. The restaurant constraint also limits profit, but since the shadow price is negative, an additional increase of the RHS reduces the profit. If the number of cuisine type drops by one, the an additional $1,660 can be made.

117) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source.

X1 = # of units from cooperative A X2 = # of units from cooperative B

120) A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment?

X1 ≥ 4 X2 ≥ 4 X3 ≥ 4 X4 ≥ 4 X1 + X2 + X3 + X4 ≤ 20

119) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions.

XA + XB ≥ 12000 XA ≤ 8000 XB ≥ 6000

29) Taco Loco should produce both ________ but should not make any ________.

Z and Y, X

86) Use the LP output to answer these two questions. (a) By how much can the amount of space decrease before there is a change in the profit? (b) What is the impact on profit if white, blue and purple stocking levels must equal at least 52 units?

a) 0 b) drops by $82.50

85) Use the LP output to answer these two questions. (a) To what value can the per bottle profit on white nail polish drop before the solution (product mix) would change? (b) By how much can the per bottle profit on purple nail polish increase before the solution (product mix) would change?

a) 145 b) 1

49) The objective function 3x + 2y + 4xy violates the assumption of ________.

additivity

83) What is the range for the shadow price for assembly?

allowable decrease = 45 - 15 = 30, and allowable increase is ∞.

28) Taco Loco should try to purchase additional ________, but should not buy more ________.

beef and cheese, beans

37) The ________ is the volume that equates total revenue with total cost.

break-even point

50) Mildred is attempting to prepare an optimal quantity of macaroni and cheese for the potluck supper this Sunday. The instructions indicate that one cup of water is needed for each box she needs to prepare. She sleeps well on Saturday night, secure in her knowledge that she knows the precise amount of water she will need the next day. This knowledge illustrates the assumption of ________.

certainty

34) A(n) ________ is a linear relationship representing a restriction on decision making.

constraint

38) A(n) ________ represents a limitation to achieving maximum profits due to limited resources.

constraint

128) Consider the following linear programming problem: MIN Z = 10x1 + 20x2 Subject to: x1 + x2 ≥ 12 2x1 + 5x2 ≥ 40 x2 ≤ 13 x1, x2 ≥ 0 At the optimal solution, what is the value of surplus associated with constraint 1 and constraint 3, respectively?

constraint 1: (0 surplus), constraint 2: (7.667 surplus)

88) Max Z = 4x1 + 3x2 Subject to: 6x1 + 2x2 ≤ 24 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0 Determine the sensitivity range for each constraint.

constraint 1: 6 - 24 constraint 2: 60 - 240

42) A(n) ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations.

decision support system, DSS

51) Tim! airlines procurement division works with their linear programming algorithm to secure contracts for gasoline for the coming year. After twenty minutes of thinking, the computer suggests that they secure 425.8125 contracts with their suppliers. This value illustrates the assumption of ________ in linear programming models.

divisibility or continuous

35) The Shadow Price in an Excel sensitivity report is found under the heading of ________ in the QM for Windows report.

dual value

44) Corner points on the boundary of the feasible solution area are called ________ points.

extreme

54) In a graphical approach to a linear programming problem, the objective function has a maximum value when it is ________ the origin.

farthest away from

37) The ________ solution area is an area bounded by the constraint equations.

feasible

46) The ________ step in formulating a linear programming model is to define the decision variables.

first

35) If at least one constraint in a linear programming model is violated, the solution is said to be ________.

infeasible

24) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection) by two hours, they should increase ________.

inspection

33) The amount in euros that a Parisian manager would be willing to pay is the ________ .

marginal value

29) A(n) ________ is a functional relationship including variables, parameters, and equations.

model

43) If the objective function is parallel to a constraint, the linear program could have ________.

multiple optimal solutions

32) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed.

network

22) The sensitivity range for a(n) ________ coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

objective function

40) The best feasible solution is ________.

optimal

38) Multiple optimal solutions can occur when the objective function line is ________ to a constraint line.

parallel

41) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique.

probabilistic

36) Total revenue minus total cost equals ________.

profit

48) The ________ property of linear programming models indicates that the rate of change, or slope, of the objective function or a constraint is constant.

proportionality or linearity

39) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis.

sensitivity

21) The sensitivity range for a constraint quantity value is also the range over which the ________ is valid.

shadow price

41) In a constraint, the ________ variable represents unused resources.

slack

33) An increase in output typically results in an increase in the ________ cost.

total variable, total

36) A graphical solution is limited to solving linear programming problems with ________ decision variables.

two

39) XY Corporation makes two products, X and Y, and uses graphical linear programming to determine their monthly product mix. This November, their only production constraint is X ≤ 75. November's production problem is ________.

unbounded

47) The management scientist constructed a linear program to help the alchemist maximize his gold production process. The computer model chugged away for a few minutes and returned an answer of infinite profit., which is what might be expected from a(n) ________ problem.

unbounded

34) The Allowable Increase in an Excel sensitivity report is found under the heading of ________ in the QM for Windows report.

upper bound

43) The databases, management science models, and internet interact with the decision maker via the ________.

user interface

111) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the United States, and $3 for every performance outside the United States. Define variables for this problem.

x = # of performances in the United States y = # of performances outside the United States

118) Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?

x = 0, y = 8, revenue = $160, s1= 0

82) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced?

x = 22.5, y = 15, Z = 1125, so profits will fall by $1350 - $1125 = $225. Students may also answer the question by determining the sensitivity range, which is from 60 to 180 hours, resulting in a profit change of 30 × $7.5 = $225.

110) Solve the following graphically: (refer to the graph) Max z = 3x1 + 4x2 s.t. x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0 What are the optimal values of x1, x2, and z?

x1 = 9, x2 = 0, z = 27

90) Max Z = 3x1 + 3x2 Subject to: 10x1 + 4x2 ≤ 60 25x1 + 50x2 ≤ 200 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient.

x1: 1.5 - 7.5, x2: 1.2 - 6.0

89) Max Z = 5x1 + 3x2 Subject to: 6x1 + 2x2 ≤ 18 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient.

x1: 2.25 - 9.0, x2: 1.667 - 6.667

19) The reduced cost (shadow price) for a positive decision variable is ________.

zero

55) The three types of linear programming constraints are ________, ________, and ________.

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