Deck 19: Linear Programming

Question 1

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

Answer 1

False

Question 2

The equation 3xy = 9 is linear.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

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 6

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

Question 7

The term isoprofit line means that all points on the line will yield the same profit.

Question 8

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

Question 9

Profit maximization, like cost minimization, could be an objective of an LP problem, but neither would be an actual decision variable.

Question 10

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

Question 11

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

Question 12

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

Question 13

A linear programming problem can have multiple optimal solutions.

Question 14

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

Question 15

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

Question 16

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

Question 17

An objective function represents a family of parallel lines.

Question 18

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

Question 19

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

Question 20

LP problems must have a single goal or objective specified.

Question 21

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

Question 22

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

A) 1A + 2B ≤ 3
B) 1A + 2B ≥ 3
C) 1A + 2B = 3
D) 1A + 2B + 3C + 4D ≤ 5
E) 1A + 2B

Question 23

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 24

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) Z = 1A + 2B - 1CD

Question 25

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

Question 26

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 27

In graphical linear programming, the objective function is:
(I) a family of parallel lines.
(II) a family of isoprofit lines.
(III) interpolated.
(IV) linear.

A) I only
B) II only
C) III and IV only
D) I, II, and IV only
E) I, II, III, and IV

Question 28

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

Question 29

What combination of x and y will yield the optimum for this problem? Maximize $Z=\$ 3 x+\$ 15 y$

$\begin{array}{l}\text{Subject to:}&2 x+4 y \leq 12 \\&5 x+2 y \leq 10\end{array}$

A) x = 2, y = 0
B) x = 0, y = 0
C) x = 0, y = 3
D) x = 1, y = 5
E) x = 0, y = 4

Question 30

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 31

Nonzero slack or surplus is associated with a binding constraint.

Question 32

For the following constraints, which point is in the feasible solution space of this maximization problem? $$\begin{aligned}14 x + 6 y & \leq 42 \\x - y & \leq 3\end{aligned}$$

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 33

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

Question 34

Which of the following choices constitutes a simultaneous solution to these equations? $$\begin{array} { l } 3 x + 2 y = 6 \\6 x + 3 y = 12\end{array}$$

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 35

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 36

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 37

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 38

Which of the following choices constitutes a simultaneous solution to these equations? $$\begin{array} { l } 3 \mathrm { x } + 4 \mathrm { y } = 10 \\5 \mathrm { x } + 4 \mathrm { y } = 14\end{array}$$

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

Question 39

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

Question 40

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

A) the solution is suboptimal.
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 41

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

A) I and II only
B) II and III only
C) I, II, and III
D) I and III only
E) I only

Question 42

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the objective function?

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

Question 43

In linear programming, a nonzero 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 44

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. 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 45

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 46

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What are optimal weekly profits?

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

Question 47

For the constraints given below, which point is in the feasible solution space of this minimization problem? $$\begin{aligned}14 x + 6 y & \geq 42 \\x + 3 y & \geq 6\end{aligned}$$

A) x = .5, y = 5
B) x = 0, y = 4
C) x = 2, y = 5
D) x = 1, y = 2
E) x = 2, y = 1

Question 48

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the Dominican bean constraint?

A) 12A + 8B ≤ 4,800
B) 8A + 12B ≤ 4,800
C) 4A + 8B ≤ 3,200
D) 8A + 4B ≤ 3,200
E) 4A + 8B ≤ 4,800

Question 49

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the Columbia bean constraint?

A) 1A + 2B ≤ 4,800
B) 12A + 8B ≤ 4,800
C) 2A + 1B ≤ 4,800
D) 8A + 12B ≤ 4,800
E) 4A + 8B ≤ 4,800

Question 50

An analyst, having solved a linear programming problem, determined that he had 10 more units of resource Q than previously believed. Upon modifying his program, he observed that the optimal solution did not change, but the value of the objective function increased by $30. This means that resource's Q's shadow price was:

A) $1.50.
B) $3.00.
C) $6.00.
D) $15.00.
E) $30.00.

Question 51

In a linear programming problem involving maximization, at least one constraint must be of the __________ type.

A) greater than or equal
B) integer
C) binary
D) less than or equal
E) surplus

Question 52

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 53

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

A) redundant constraint.
B) binding constraint.
C) nonbinding constraint.
D) feasible solution constraint.
E) constraint that equals zero.

Question 54

In a linear programming problem, the objective function was specified as follows: Z = 2A + 4B + 3C
The optimal solution calls for A to equal 4, B to equal 6, and C to equal 3. It has also been determined that the coefficient associated with A can range from 1.75 to 2.25 without the optimal solution changing. This range is called A's:

A) range of optimality.
B) range of feasibility.
C) shadow price.
D) slack.
E) surplus.

Question 55

In the graphical approach to linear programming, finding values for the decision variables at the intersection of corners requires the solving of:

A) linear constraints.
B) surplus variables.
C) slack variables.
D) simultaneous equations.
E) binding constraints.

Question 56

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 57

What combination of x and y will provide a minimum for this problem? Minimize $Z = \$ 3 x + \$ 15 y$
$\begin{array} { l } \text{Subject to:}&2 x + 4 y \geq 12 \\&5 x + 2 y \geq 10\end{array}$

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 58

A redundant constraint is one that:

A) is parallel to the objective function.
B) has no coefficient for at least one decision variable.
C) has a zero coefficient for at least one decision variable.
D) has multiple coefficients for at least one decision variable.
E) does not form a unique boundary of the feasible solution space.

Question 59

In a linear programming problem involving minimization, at least one constraint must be of the __________ type.

A) less than or equal
B) integer
C) greater than or equal
D) binary
E) slack

Question 60

The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. Which of the following is not a feasible production combination?

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

Question 61

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. Which of the following is not a feasible production combination?

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

Question 62

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. 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 63

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the objective function?

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

Question 64

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. Which of the following is not a feasible production combination?

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

Question 65

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. Which of the following is not a feasible production/sales combination?

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

Question 66

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What are optimal profits for today's production run?

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

Question 67

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What are optimal daily profits?

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

Question 68

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. Which of the following is not a feasible production combination?

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

Question 69

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. 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 70

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What is the time constraint?

A) 2L + 3D ≤ 480
B) 2L + 4D ≤ 480
C) 3L + 2D ≤ 480
D) 4L + 2D ≤ 480
E) 5L + 3D ≤ 480

Question 71

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the production time constraint (in minutes)?

A) 2R + 3S ≤ 720
B) 2R + 5S ≤ 720
C) 3R + 2S ≤ 720
D) 3R + 5S ≤ 720
E) 5R + 5S ≤ 720

Question 72

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. 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 nor carbonated water
E) cannot be determined exactly

Question 73

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What are optimal weekly profits?

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

Question 74

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the assembly time constraint (in hours)?

A) 1A + 1B ≤ 800
B) .25A + .5B ≤ 800
C) .5A + .25B ≤ 800
D) 1A + .5B ≤ 800
E) .25A + 1B ≤ 800

Question 75

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What is the sugar constraint (in tablespoons)?

A) 6B + 3C ≤ 4,800
B) 1B + 1C ≤ 4,800
C) 2B + 4C ≤ 4,800
D) 4B + 2C ≤ 4,800
E) 2B + 3C ≤ 4,800

Question 76

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What are optimal daily profits?

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

Question 77

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What is the objective function?

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

Question 78

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What is the objective function?

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

Question 79

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the objective function?

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

Question 80

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. For the production combination of 1,400 A-100s and 900 B-200s, 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