AGEC 3413 Exam 2

________ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

In a(n) ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values.

C

Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of water-base paint, which constraint correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000

D

The branch and bound method of solving linear integer programming problems is: A) an integer method. B) a relaxation method. C) a graphical solution. D) an enumeration method.

D

Data envelopment analysis indicates which type of service unit makes the highest profit. True or False

FALSE

Transportation problems can have solution values that are non-integer and must be rounded. True or False

FALSE

A mixed integer program has only integers as a solution they are simply mixed, as opposed to an integer program where they are specific to the decision variables. True or False

False

The three types of integer programming models are total, 0-1, and mixed. True or False

TRUE

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

audience exposure

There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter.

transportation problem

Rounding a noninteger solution ________ to the nearest integer value will likely result in an infeasible solution.

up

A balanced transportation model should have ________ constraints.

= or "equal to"

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit? A) $380 B) $400 C) $420 D) $440

A

Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value.

A

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never

A

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

A

In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

A

Let: rj = regular production quantity for period j, oj = overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj.

A

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected. A) exactly 1, 2 B) exactly 2, 4 C) at least 2, 4 D) at most 1, 2

B

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible

B

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

B

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already

B

In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

B

In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory.

B

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above

B

The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending.

B

________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

Blending

A systematic approach to model formulation is to first: A) construct the objective function. B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint.

C

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2." The constraint for this requirement can be written as: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0.

C

Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) <

C

For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down

C

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

C

In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

C

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? A) x1 + x2 + x5 ≤ 1 B) x1 + x2 + x5 ≥ 1 C) x1 + x5 ≤ 1, x2 + x5 ≤ 1 D) x1 - x5 ≤ 1, x2 - x5 ≤ 1

C

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? A) X2 ≤ 10000, X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000, X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000, 47.25 X2 + 110X3 ≤ 350

C

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000

C

Max Z = 13x1 + 8x2 Subject to: 15x1 + 12x2 ≤ 144 7x1 + 9x2 ≤ 64 x1, x2 ≥ 0 and integer What is the optimal solution? A) x1 = 5, x2 = 6, Z = 113 B) x1 = 7, x2 = 7, Z = 147 C) x1 = 9, x2 = 0, Z = 117 D) x1 = 0, x2 = 15, Z = 120

C

Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers

D

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal

D

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

D

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also

D

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0

D

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11+ x21= 11000

D

Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous

D

A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints. True or False

FALSE

A data envelopment analysis with an objective function value of 0.8 means the company is more efficient than its competitors since it expends only 80% of the effort to achieve the same results. True or False

FALSE

A linear programming model of a media selection problem is used to determine the relative value of each advertising media. True or False

FALSE

Diet problems usually maximize nutritional value. True or False

FALSE

Double-subscripted variables are required when there are two decision variables. True or False

FALSE

Fractional relationships among variables are considered standard form in a blending problem. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint. True or False

FALSE

In Excel, a binary constraint in cell A1 is created using the =BIN($A$1) formula. True or False

FALSE

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. True or False

FALSE

In a classic blending problem, revenue is maximized by subtracting cost from profit. True or False

FALSE

In a mixed integer model, all decision variables have integer solution values. True or False

FALSE

In a mixed integer model, the solution values of the decision variables are 0 or 1. True or False

FALSE

In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). True or False

FALSE

In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs. True or False

FALSE

In most media selection decisions, the objective of the decision maker is to minimize cost. True or False

FALSE

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate. True or False

FALSE

Product mix problems cannot have greater-than-or-equal-to (≥) constraints. True or False

FALSE

The branch and bound solution method cannot be applied to 0-1 integer programming problems. True or False

FALSE

The constraint x + y = z is written in standard form. True or False

FALSE

The management scientist's fiancé informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize profit. True or False

FALSE

When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.

SUMPRODUCT

A company can use regular time, overtime, and subcontracting in any amount over the one-year production planning horizon to meet forecasted demand. If they develop the plan using linear programming, they will have a total of 36 decision variables that govern the amount produced by these three methods. True or False

TRUE

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values. True or False

TRUE

Blending problems usually require algebraic manipulation in order to write the LP in "standard form." True or False

TRUE

Data envelopment analysis problems are usually maximization problems. True or False

TRUE

Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint. True or False

TRUE

In a 0-1 integer model, the solution values of the decision variables are 0 or 1. True or False

TRUE

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. True or False

TRUE

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally, the objective is to maximize the audience exposure. True or False

TRUE

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. True False

TRUE

In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. True or False

TRUE

In a total integer model, all decision variables have integer solution values. True or False

TRUE

In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). True or False

TRUE

In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). True or False

TRUE

Integer constraints are entered in the inequality dialog box within Excel's Solver routine. True or False

TRUE

One type of constraint in an integer program is a multiple-choice constraint. True or False

TRUE

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. True or False

TRUE

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables. True or False

TRUE

The divisibility assumption is violated by integer programming. True or False

TRUE

The feasible region in an integer programming graph is composed of a lattice of points. True or False

TRUE

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several unsold half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible. True or False

TRUE

The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions.

branch and bound

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a(n) ________ constraint.

conditional

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a(n) ________ constraint."

contingency or mutually exclusive

In a balanced transportation model, supply equals ________.

demand

Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem.

diet

Rounding a noninteger solution ________ to the nearest integer guarantees a feasible, but perhaps suboptimal solution to an integer programming situation.

down

Data envelopment analysis indicates the relative ________ of a service unit compared with others.

efficiency or productivity

In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

media selection

The objective function of a diet problem is usually to ________ subject to nutritional requirements.

minimize costs

A(n) ________ integer model allows for the possibility that some decision variables are not integers.

mixed

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a(n) ________ constraint.

multiple-choice

In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a(n) ________ constraint.

multiple-choice

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a(n) ________ constraint.

mutually exclusive

In a data envelopment analysis, it is customary to scale input process so that the total value of a unit's inputs equals ________.

one

Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

product mix

Investment problems maximize ________.

return on investments

The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

standard form

In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________.

x1 + x2 = 1

In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________.

x1 = x2