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

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y = 360 all variables >=0 The maximum possible profit for the objective function is

1520.

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

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

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

What are the four requirements of a linear programming problem?

an objective, constraints, alternatives, and linearity

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

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

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.

When using a graphical solution procedure, the region bounded by the set of constraints is called the

feasible region.

In linear programming, a solution that does not simultaneously satisfy all constraints is called an

infeasible solution.

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

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 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.

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

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 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.