Deck 22: Linear Programming

Question 1

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

Answer 1

False

Question 2

Which of the following statements regarding linear programming is NOT true?

A)A parameter is also known as a decision variable.
B)Linearity assumes proportionality and additivity.
C)The product-mix problem is a one-period type of aggregate planning problem.
D)One reasonable sequence for formulating a model is defining the decision variables,writing out the objective function,and writing out the constraints.

Answer 2

A

Question 3

A site manager has three day laborers available for eight hours each and a burning desire to maximize his return on their wages.The site manager uses linear programming to assign them to two tasks and notes that he has enough work to occupy 21 labor hours.The linear program that the site manager has constructed has

A)slack.
B)surplus.
C)a positive shadow price for labor.
D)no feasible solution.

Answer 3

D

Question 4

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

Question 5

For the line that has the equation 4X1 + 8X2 = 88,an axis intercept is

A)(0,22).
B)(6,0).
C)(6,22).
D)(0,11).

Question 6

In linear programming,each parameter is assumed to be known with certainty.

Question 7

Linear programming is useful for allocating scarce resources among competing demands.

Question 8

One assumption of linear programming is that a decision maker cannot use negative quantities of the decision variables.

Question 9

A binding constraint is the amount by which the left-hand side falls short of the right-hand side.

Question 10

Only corner points should be considered for the optimal solution to a linear programming problem.

Question 11

The objective function Maximize Z = 3x2 = 4y is appropriate.

Question 12

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is correct?

A)The manager has four decision variables.
B)The manager has three constraints.
C)The manager has three decision variables.
D)The manager can solve this problem graphically.

Question 13

Consider a corner point to a linear programming problem,which lies at the intersection of the following two constraints: 6X1 + 15X2 < 390
2X1 + X2 < 50
Which of the following statements about the corner point is true?

A)X1 < 21
B)X1 > 25
C)X1 < 10
D)X1 > 17

Question 14

Which of the following statements regarding linear programming is NOT true?

A)A linear programming problem can have more than one optimal solution.
B)Most real-world linear programming problems are solved on a computer.
C)If a binding constraint were relaxed,the optimal solution wouldn't change.
D)A surplus variable is added to a > constraint to convert it to an equality.

Question 15

A binding constraint has slack but does not have surplus.

Question 16

Suppose that the optimal values of the decision variables to a two-variable linear programming problem remain the same as long as the slope of the objective function lies between the slopes of the following two constraints: 2X1 + 3X2 < 26
2X1 + 2X2 < 20
The current objective function is:
8X1 + 9X2 = Z
Which of the following statements about the range of optimality on c1 is TRUE?

A)0 < c1 < 2
B)2 < c1 < 6
C)6 < c1 < 9
D)9 < c1 < 12

Question 17

A constraint is a limitation that restricts the permissible choices.

Question 18

The simplex method is an interactive algebraic procedure for solving linear programming problems.

Question 19

A manager is interested in using linear programming to analyze production for the ensuing week.She knows that it will take exactly 1.5 hours to run a batch of product A and that this batch will consume two tons of sugar.This is an example of the linear programming assumption of

A)linearity.
B)certainty.
C)continuous variables.
D)whole numbers.

Question 20

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

Question 21

A(n)________ is a value that the decision maker cannot control and that does not change when the solution is implemented.

Question 22

The ________ is the upper and lower limit over which the optimal values of the decision variables remain unchanged.

Question 23

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

Question 24

________ are the limitations that restrict the permissible choices for the decision variables.

Question 25

The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

Question 26

A modeler is limited to two or fewer decision variables when using the ________.

Question 27

A(n)________ is the marginal improvement in the objective function value caused by relaxing a constraint by one unit.

Question 28

The ________ problem is a one-period type of aggregate planning problem,the solution of which yields optimal output quantities of a group of products or services,subject to resource capacity and market demand conditions.

Question 29

Each coefficient or given constant is known by the decision maker with ________.

Question 30

In linear programming,a ________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

Question 31

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that

A)the next worker that offers to work an extra 8 hours should receive at least $80.
B)you can send someone home 6 hours early and still pay them the $60 they would have earned while on the clock.
C)you would be willing pay up to $60 for someone to work another 6 hours.
D)you would lose $80 if one of your workers missed an entire 8 hour shift.

Question 32

________ represent choices the decision maker can control.

Question 33

________ is an assumption that the decision variables must be either positive or zero.

Question 34

The ________ represents all permissible combinations of the decision variables in a linear programming model.

Question 35

________ is the amount by which the left-hand side falls short of the right-hand side in a linear programming model.

Question 36

For an = constraint,only points ________ are feasible solutions.

Question 37

A(n)________ forms the optimal corner and limits the ability to improve the objective function.

Question 38

________ is useful for allocating scarce resources among competing demands.

Question 39

________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.

Question 40

If merely rounding up or rounding down a result for a decision variable is not sufficient when they must be expressed in whole units,then a decision maker might instead use ________ to analyze the situation.

Question 41

________ occurs in a linear programming problem when the number of nonzero variables in the optimal solution is fewer than the number of constraints.

Question 42

Briefly describe the meaning of a shadow price.Provide an example of how a manager could use information about shadow prices to improve operations?

Question 43

The interval over which the right-hand-side parameter can vary while its shadow price remains valid is the ________.

Question 44

What is the meaning of a slack or surplus variable?

Question 45

What are the assumptions of linear programming? Provide examples of each.

Question 46

Provide three examples of operations management decision problems for which linear programming can be useful,and why.

Question 47

What are some potential abuses or misuses of linear programming (beyond violation of basic assumptions)?