Question 1

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)?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. What are profits for the optimal production combination?

Accepted Answer

A)  $800 
B)  $500 
C)  $640 
D)  $620 
E)  $600

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

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

Accepted Answer

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 9

A novice linear programmer is dealing with a three-decision-variable problem. To compare the attractiveness of various feasible decision-variable combinations, values of the objective function at corners are calculated. This is an example of:

Accepted Answer

A)  empiritation. 
B)  explicitation. 
C)  evaluation. 
D)  enumeration. 
E)  elicitation.

Question 10

Profit maximization could be an objective of an LP problem; but cost minimization cannot be the objective of an LP problem.

Accepted Answer

A) True 
 B)False

Question 11

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?

Accepted Answer

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 12

In linear programming, a nonzero reduced cost is associated with a:

Accepted Answer

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 13

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?

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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?

Accepted Answer

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

Question 16

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)?

Accepted Answer

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 17

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

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

Question 20

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)?

Accepted Answer

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

Exam 25: Linear Programming

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

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

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

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

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

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

A novice linear programmer is dealing with a three-decision-variable problem. To compare the attractiveness of various feasible decision-variable combinations, values of the objective function at corners are calculated. This is an example of:

Profit maximization could be an objective of an LP problem; but cost minimization cannot be the objective of an LP problem.

In linear programming, a nonzero reduced cost is associated with a:

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

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

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

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