Deck 19: Linear Programming

Question 1

Graphical linear programming can handle problems that involve any number of decision variables.

Answer 1

False

Question 2

The equation 5x + 7y = 10 is linear.

Answer 2

True

Question 3

LP problems must have a single goal or objective specified.

Answer 3

True

Question 4

An objective function represents a family of parallel lines.

Question 5

The term "iso-profit" line means that all points on the line will yield the same profit.

Question 6

A maximization problem may be characterized by all greater than or equal to constraints.

Question 7

A change in the value of an objective function coefficient does not change the optimal solution.

Question 8

Linear programming techniques will always produce an optimal solution to an LP problem.

Question 9

The term "range of optimality" refers to a constraint's right-hand side quantity.

Question 10

A linear programming problem can have multiple optimal solutions.

Question 11

The term "range of feasibility" refers to coefficients of the objective function.

Question 12

The value of an objective function decreases as it is moved away from the origin.

Question 13

A shadow price indicates how much a one-unit decrease/increase in the right-hand side value of a constraint will decrease/increase the optimal value of the objective function.

Question 14

If a single optimal solution exists to a graphical LP problem, it will exist at a corner point.

Question 15

The equation 3xy = 9 is linear.

Question 16

An example of a decision variable in an LP problem is profit maximization.

Question 17

Constraints limit the alternatives available to a decision-maker, removing constraints adds viable alternative solutions.

Question 18

The feasible solution space only contains points that satisfy all constraints.

Question 19

The feasible solution space is the set of all feasible combinations of decision variables as defined by only binding constraints.

Question 20

The simplex method is a general-purpose LP algorithm that can be used for solving only problems with more than six variables.

Question 21

The linear optimization technique for allocating constrained resources among different products is:

A)linear regression analysis
B)linear disaggregation
C)linear decomposition
D)linear programming
E)linear tracking analysis

Question 22

Non-binding constraints are not associated with the feasible solution space; i.e., they are redundant and can be eliminated from the matrix.

Question 23

Coordinates of all corner points are substituted into the objective function when we use the approach called:

A)Least Squares
B)Regression
C)Enumeration
D)Graphical Linear Programming
E)Constraint Assignment

Question 24

Every change in the value of an objective function coefficient will lead to changes in the optimal solution.

Question 25

The logical approach, from beginning to end, for assembling a linear programming model begins with:

A)identifying the decision variables
B)identifying the objective function
C)specifying the objective function parameters
D)identifying the constraints
E)specifying the constraint parameters

Question 26

Which of the following could not be a linear programming problem constraint?

A)1A + 2B $\le$ 3
B)1A + 2B $\ge$ 3
C)1A + 2B = 3
D)1A + 2B + 3C + 4D $\le$ 5
E)1 A + 2B

Question 27

When a change in the value of an objective function coefficient remains within the range of optimality, the optimal solution would also remain the same.

Question 28

Non-zero slack or surplus is associated with a binding constraint.

Question 29

In graphical linear programming, when the objective function is parallel to one of the binding constraints, then:

A)the solution is sub-optimal
B)multiple optimal solutions exist
C)a single corner point solution exists
D)no feasible solution exists
E)the constraint must be changed or eliminated

Question 30

In graphical linear programming the objective function is:

A)linear
B)a family of parallel lines
C)a family of iso-profit lines
D)all of the above
E)none of the above

Question 31

Which of the choices below constitutes a simultaneous solution to these equations?

A)x = 2, y = .5
B)x = 4, y = -.5
C)x = 2, y = 1
D)x = y
E)y = 2x

Question 32

Using the enumeration approach, optimality is obtained by evaluating every coordinate.

Question 33

Which of the choices below constitutes a simultaneous solution to these equations?

A)x = 1, y = 1.5
B)x = .5, y = 2
C)x = 0, y = 3
D)x = 2, y = 0
E)x = 0, y = 0

Question 34

What combination of x and y will yield the optimum for this problem?

A)x = 2, y = 0
B)x = 0, y = 0
C)x = 0, y = 3
D)x = 1, y = 5
E)none of the above

Question 35

For the products A, B, C and D, which of the following could be a linear programming objective function?

A)Z = 1A + 2B + 3C + 4D
B)Z = 1A + 2BC + 3D
C)Z = 1A + 2AB + 3ABC + 4ABCD
D)Z = 1A + 2B/C + 3D
E)all of the above

Question 36

Which of the following is not a component of the structure of a linear programming model?

A)Constraints
B)Decision variables
C)Parameters
D)A goal or objective
E)Environmental uncertainty

Question 37

Which objective function has the same slope as this one: $4x + $2y = $20?

A)$4x + $2y = $10
B)$2x + $4y = $20
C)$2x - $4y = $20
D)$4x - $2y = $20
E)$8x + $8y = $20

Question 38

The region which satisfies all of the constraints in graphical linear programming is called the:

A)optimum solution space
B)region of optimality
C)lower left hand quadrant
D)region of non-negativity
E)feasible solution space

Question 39

In the range of feasibility, the value of the shadow price remains constant.

Question 40

For the constraints given below, which point is in the feasible solution space of this maximization problem?

A)x = 1, y = 5
B)x = -1, y = 1
C)x = 4, y = 4
D)x = 2, y = 1
E)x = 2, y = 8

Question 41

What is the objective function?

A)$1 A + $2 B = Z
B)$12 A + $8 B = Z
C)$2 A + $1 B = Z
D)$8 A + $12 B = Z
E)$4 A + $8 B = Z

Question 42

Consider the linear programming problem below: Determine the optimum amounts of x and y in terms of cost minimization.What is the minimum cost?

Question 43

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

A)1
B)2
C)3
D)4
E)unlimited

Question 44

A shadow price reflects which of the following in a maximization problem?

A)marginal cost of adding additional resources
B)marginal gain in the objective that would be realized by adding one unit of a resource
C)net gain in the objective that would be realized by adding one unit of a resource
D)marginal gain in the objective that would be realized by subtracting one unit of a resource
E)expected value of perfect information

Question 45

In linear programming, a non-zero reduced cost is associated with a:

A)decision variable in the solution
B)decision variable not in the solution
C)constraint for which there is slack
D)constraint for which there is surplus
E)constraint for which there is no slack or surplus

Question 46

Consider the following linear programming problem: Solve the values of x and y that will maximize revenue.What revenue will result?

Question 47

What is the Dominican bean constraint?

A)12A + 8B $\le$ 4,800
B)8A + 12B $\le$ 4,800
C)4A + 8B $\le$ 3,200
D)8A + 4B $\le$ 3,200
E)4A + 8B $\le$ 4,800

Question 48

The theoretical limit on the number of constraints that can be handled by the simplex method in a single problem is:

A)1
B)2
C)3
D)4
E)unlimited

Question 49

What are optimal weekly profits?

A)$0
B)$400
C)$700
D)$800
E)$900

Question 50

In linear programming, sensitivity analysis is associated with: (I) objective function coefficient
(II) right-hand side values of constraints
(III) constraint coefficient

A)I and II
B)II and III
C)I, II and III
D)I and III
E)none of the above

Question 51

A constraint that does not form a unique boundary of the feasible solution space is a:

A)redundant constraint
B)binding constraint
C)non-binding constraint
D)feasible solution constraint
E)constraint that equals zero

Question 52

What combination of x and y will provide a minimum for this problem?

A)x = 0, y = 0
B)x = 0, y = 3
C)x = 0, y = 5
D)x = 1, y = 2.5
E)x = 6, y = 0

Question 53

Solve the following linear programming problem:

Question 54

Which of the following is not a feasible production combination?

A)0 A & 0 B
B)0 A & 400 B
C)200 A & 300 B
D)400 A & 0 B
E)400 A & 400 B

Question 55

Given this problem:

Question 56

For the constraints given below, which point is in the feasible solution space of this minimization problem?

A)x = 0.5, y = 5.0
B)x = 0.0, y = 4.0
C)x = 2.0, y = 5.0
D)x = 1.0, y = 2.0
E)x = 2.0, y = 1.0

Question 57

What is the Columbia bean constraint?

A)1 A + 2 B $\le$ 4,800
B)12 A + 8 B $\le$ 4,800
C)2 A + 1 B $\le$ 4,800
D)8 A + 12 B $\le$ 4,800
E)4 A + 8 B $\le$ 4,800

Question 58

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute per unit for packing.Product B requires two minutes per unit for molding, four minutes per unit for painting, and three minutes per unit for packing.There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing.Both products have profits of $1.50 per unit.
(A) What combination of A and B will maximize profit?
(B) What is the maximum possible profit?
(C) How much of each resource will be unused for your solution?

Question 59

A small firm makes three products, which all follow the same three step process, which consists of milling, inspection, and drilling.Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling.The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling.Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit.
Use the following computer output to find the optimum mix of products in terms of maximizing contributions to profits for the next period.
PROBLEM TITLE: LINEAR PROGRAMMING
PROBLEM IS A MAX WITH 3 VARIABLES AND 3 CONSTRAINTS.

Question 60

For the production combination of 0 American and 400 British, which resource is "slack" (not fully used)?

A)Colombian beans (only)
B)Dominican beans (only)
C)both Colombian beans and Dominican beans
D)neither Colombian beans nor Dominican beans
E)cannot be determined exactly

Question 61

What are optimal weekly profits?

A)$10,000
B)$4,600
C)$2,500
D)$5,200
E)$6,400

Question 62

What is the time constraint?

A)2 L + 3 D $\le$ 480
B)2 L + 4 D $\le$ 480
C)3 L + 2 D $\le$ 480
D)4 L + 2 D $\le$ 480
E)5 L + 3 D $\le$ 480

Question 63

For the production combination of 1,400 A-100's and 900 B-200's which resource is "slack" (not fully used)?

A)circuit boards (only)
B)assembly time (only)
C)both circuit boards and assembly time
D)neither circuit boards nor assembly time
E)cannot be determined exactly

Question 64

Which of the following is not a feasible production combination?

A)0 L & 0 D
B)0 L & 120 D
C)90 L & 75 D
D)135 L & 0 D
E)135 L & 120 D

Question 65

Which of the following is not a feasible production combination?

A)0 B & 0 C
B)0 B & 1,100 C
C)800 B & 600 C
D)1,100 B & 0 C
E)0 B & 1,400 C

Question 66

What is the objective function?

A)$2 L + $3 D = Z
B)$2 L + $4 D = Z
C)$3 L + $2 D = Z
D)$4 L + $2 D = Z
E)$5 L + $3 D = Z

Question 67

What is the objective function?

A)$0.30 B + $0.20 C = Z
B)$0.60 B + $0.30 C = Z
C)$0.20 B + $0.30 C = Z
D)$0.20 B + $0.40 C = Z
E)$0.10 B + $0.10 C = Z

Question 68

For the production combination of 180 Root beer and 0 Sassafras soda, which resource is "slack" (not fully used)?

A)production time (only)
B)carbonated water (only)
C)both production time and carbonated water
D)neither production time and carbonated water
E)cannot be determined exactly

Question 69

Which of the following is not a feasible production combination?

A)0 R & 0 S
B)0 R & 240 S
C)180 R & 120 S
D)300 R & 0 S
E)180 R & 240 S

Question 70

What is the assembly time constraint (in hours)?

A)1 A + 1 B $\le$ 800
B)0.25 A + 0.5 B $\le$ 800
C)0.5 A + 0.25 B $\le$ 800
D)1 A + 0.5 B $\le$ 800
E)0.25 A + 1 B $\le$ 800

Question 71

What is the objective function?

A)$4.00 A + $1.00 B = Z
B)$0.25 A + $1.00 B = Z
C)$1.00 A + $4.00 B = Z
D)$1.00 A + $1.00 B = Z
E)$0.25 A + $0.50 B = Z

Question 72

What are optimal profits for today's production run?

A)$580
B)$340
C)$220
D)$380
E)$420

Question 73

What is the production time constraint (in minutes)?

A)2 R + 3 S $\le$ 720
B)2 R + 5 S $\le$ 720
C)3 R + 2 S $\le$ 720
D)3 R + 5 S $\le$ 720
E)5 R + 5 S $\le$ 720

Question 74

For the production combination of 600 bagels and 800 croissants, which resource is "slack" (not fully used)?

A)flour (only)
B)sugar (only)
C)flour and yeast
D)flour and sugar
E)yeast and sugar

Question 75

For the production combination of 135 Lite and 0 Dark which resource is "slack" (not fully used)?

A)time (only)
B)malt extract (only)
C)both time and malt extract
D)neither time nor malt extract
E)cannot be determined exactly

Question 76

Which of the following is not a feasible production/sales combination?

A)0 A & 0 B
B)0 A & 1,000 B
C)1,800 A & 700 B
D)2,500 A & 0 B
E)100 A & 1,600 B

Question 77

What are optimal daily profits?

A)$0
B)$240
C)$420
D)$405
E)$505

Question 78

What are optimal daily profits?

A)$960
B)$1,560
C)$1,800
D)$1,900
E)$2,520

Question 79

What is the sugar constraint (in tablespoons)?

A)6 B + 3 C $\le$ 4,800
B)1 B + 1 C $\le$ 4,800
C)2 B + 4 C $\le$ 4,800
D)4 B + 2 C $\le$ 4,800
E)2 B + 3 C $\le$ 4,800

Question 80

What is the objective function?

A)$4 R + $6 S = Z
B)$2 R + $3 S = Z
C)$6 R + $4 S = Z
D)$3 R + $2 S = Z
E)$5 R + $5 S = Z