Module B
An LP modeler examines her sensitivity report and notes that the final value for item X is 200, and the shadow price is $2 with an allowable increase of 10 and an allowable decrease of 25. Which of the following statements is best?
$2 is the most the LP modeler should be willing to pay for an additional unit of item X.
Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y = 360 all variables ³ 0 Which of the following points (X,Y) is not feasible? (0,100) (70,70) (100,10) (20,90)
(70,70)
A seamstress has 30 yards of cloth and 20 yards of thread to make small, medium, or large shirts. Each small shirt takes 0.75 yards of cloth and 0.5 yards of thread; each medium shirt takes 1 yard of cloth and 0.7 yards of thread, and each large shirt takes 1.2 yards of cloth and 0.9 yards of thread. Each type of shirt takes 30 minutes to sew and the seamstress has 16 hours of time she can devote to sewing. A large shirt sells for $15, a medium for $12, and a small for $10. Using S for small, M for medium, L for large, C for cloth, T for thread, and H for hours, what is an appropriate constraint for this problem?
0.75S+1M+1.2L < 30
Consider the following linear programming problem: Maximize 4X + 10Y Subject to: 3X + 4Y = 480 4X + 2Y = 360 all variables ³ 0 The feasible corner points are (48,84), (0,120), (0,0), and (90,0). What is the maximum possible value for the objective function?
1200
If A, B, and C are variables, which of the following functions is NOT linear? A. A B. ABC C. 2A + 3B + 6C D. 14Aminus−4B + C
ABC
A manager builds an LP model and determines the values of the decision variables that yield an optimal solution. If one objective function coefficient is increased or decreased within its allowable range, the optimal objective function value will not change.
False
The iso-profit solution method can only be used to solve maximization problems.
False A minimizing problem can always be rewritten as a maximizing problem.
Any linear programming problem can be solved using the graphical solution.
False The graphical method is used for 2-dimensional problems (2 decision variables).
A constraint is a mathematical expression in linear programming that maximizes or minimizes some quantity.
False This is describing an objective function.
The objective function shown is a legitimate expression in linear programming: Max Profit = $7X + $8Y + $5XY.
False This is not a linear mathematical equation.
An objective function is necessary in a maximization problem but is not required in a minimization problem.
False Without objective function, what is the criterion for problem solution?
A seamstress has 30 yards of cloth and 20 yards of thread to make small, medium, or large shirts. Each small shirt takes 0.75 yards of cloth and 0.5 yards of thread; each medium shirt takes 1 yard of cloth and 0.7 yards of thread, and each large shirt takes 1.2 yards of cloth and 0.9 yards of thread. Each type of shirt takes 30 minutes to sew and the seamstress has 16 hours of time she can devote to sewing. A large shirt sells for $15, a medium for $12, and a small for $10. Using S for small, M for medium, L for large, C for cloth, T for thread, and H for hours, what is an appropriate objective function for this problem?
Max Profit=15L+12M+10S
Which of the following statements about linear programming is NOT correct? A. The feasible region is determined the same way for a minimization problem as for a maximization problem. B. LP problems can be structured to minimize costs as well as maximize profits. C. Minimization problems are often unbounded inward. D. The iso-cost approach attempts to move the objective function in towards the origin as far as possible.
Minimization problems are often unbounded inward.
What of the following statements about LP sensitivity analysis is NOT true?
Sensitivity information applies to simultaneous changes in several input data values.
The simplex method of linear programming is valuable when
There are more than two decision variables.
A manager builds an LP model and determines the values of the decision variables that yield an optimal solution. If one objective function coefficient is increased or decreased within its allowable range, the optimal amounts of the decision variables will not change.
True
The decision variables in a profit maximization product mix problem must all be positive.
True
The feasible region includes the edges and the corners defined by all "less than or equal to" constraints.
True
The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming.
True
In linear programming, choices available to a decision maker are called
decision variables.
The graphical solution to a linear programming problem can only be used when there are two
decision variables.
The feed-mix problem from agricultural applications is a special case of the more general
diet problem.
When using the graphical method of linear programming
each decision variable has its own dimension in the graph.
In linear programming, a solution that does not simultaneously satisfy all constraints is called an
infeasible solution.
What tool does American Airlines use to schedule flights?
linear programming
The product-mix, diet, and labor scheduling LP formulations typically have ________, ________, and ________ objectives, respectively.
maximization, minimization, minimization
In a typical product-mix problem in linear programming, the objective is to
maximize profit
A feasible solution to a linear programming problem
must satisfy all of the problem's constraints simultaneously.
What is a mathematical expression in linear programming that maximizes or minimizes some quantity?
objective function
Which of the following is a mathematical expression in linear programming that maximizes or minimizes some quantity? shadow price decision variables constraints objective function
objective function
Which of the following is an approach to solving a linear programming minimization problem graphically? A. iso-profit B. dual value C. iso-cost D. sensitivity analysis
iso-cost
Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y = 360 all variables ³ 0 The maximum possible profit for the objective function is
1520.
The value of one additional unit of a resource in a linear programming model is the shadow price.
True
Which company developed VOLCANO (Volume, Location, and Aircraft Network Optimization), an LP-based optimization system?
UPS
Which of the following is NOT considered to be a resource for a firm? A. machinery B. accounts payable C. time D. labor
accounts payable
What are the four requirements of a linear programming problem?
an objective, constraints, alternatives, and linearity
In linear programming, what are restrictions that limit the degree to which a manager can pursue an objective?
constraints
Via computer, the simplex method methodically examines ________ to search for the optimal solution of an LP problem.
corner points
Which of the following is NOT a property of linear programming problems? a. optimization of some objective b. one course of action c. the presence of restrictions d. usage of only linear equations and inequalities
one course of action
In linear programming, what is a numerical value that is given in a model?
parameter
In the objective function Max Z = 8U+4C+2O, the number 8 is a
parameter.
What is the value of one additional unit of a scarce resource in LP?
shadow price
What is the name of the algorithm that solves linear programming problems of all sizes?
simplex method
In linear programming, what is another name for sensitivity analysis?
postoptimality analysis
Two or more products are produced using limited resources. The firm would like to determine how many units of each product it should produce to maximize overall profit given its limited resources. This situation describes what type of problem in linear programming?
product-mix
Linear programming is a mathematical technique designed to help operations managers plan and make decisions necessary to allocate
resources
In a typical product-mix problem in linear programming, each general constraint states that
the amount of a resource used less than or equals ≤ the amount of resource available.
In a typical product-mix problem in linear programming, the variables are defined as
the number of units of each product produced.
Which of the following would likely NOT represent an application of linear programming in operations management? A. allocating space for a tenant mix in a new shopping mall so as to minimize revenues to the leasing company B. scheduling school buses to minimize the total distance traveled when carrying students C. allocating police patrol units to high crime areas to minimize response time to 911 calls D. scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor
allocating space for a tenant mix in a new shopping mall so as to minimize revenues to the leasing company
An optimal solution to a linear programming problem MUST lie
at the intersection of at least two constraints.
Which of the following is NOT an example of an application of linear programming? a. picking blends of raw materials in feed mills to produce finished feed combinations at minimum cost b. calculating the wages for an hourly worker if the time worked is unknown c. scheduling school buses to minimize distance traveled when carrying students d. scheduling tellers at banks so service requirements are met during each hour of the day while minimizing the total cost of labor
calculating the wages for an hourly worker if the time worked is unknown
When using a graphical solution procedure, the region bounded by the set of constraints is called the
feasible region.