Question 1

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

Accepted Answer

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

Question 2

LP problems must have a single goal or objective specified.

Accepted Answer

A) True 
 B)False

Question 3

The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the maximum profit?

Accepted Answer

A)  $0 
B)  $30,000 
C)  $42,000 
D)  $45,000 
E)  $54,000 
A)  $0 
B)  $30,000 
C)  $42,000 
D)  $45,000 
E)  $54,000

Question 4

A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units.
What is the slack (unused amount) for each resource for the optimum production combination?

Accepted Answer

S(I) = 0;

Question 5

The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the objective function?

Accepted Answer

A)  Z = $150K + $300Q 
B)  Z = $500K + $300Q 
C)  Z = $300K + $150Q 
D)  Z = $300K + $500Q 
E)  Z = $100K + $90Q 
A)  Z = $150K + $300Q 
B)  Z = $500K + $300Q 
C)  Z = $300K + $150Q 
D)  Z = $300K + $500Q 
E)  Z = $100K + $90Q

Question 6

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 is the constraint for sugar?

Accepted Answer

A)  2D + 3C ≤ 4,800 
B)  6D + 8C ≤ 4,800 
C)  1D + 2C ≤ 4,800 
D)  3D + 2C ≤ 4,800 
E)  4D + 5C ≤ 4,800 
A)  2D + 3C ≤ 4,800 
B)  6D + 8C ≤ 4,800 
C)  1D + 2C ≤ 4,800 
D)  3D + 2C ≤ 4,800 
E)  4D + 5C ≤ 4,800

Question 7

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

Accepted Answer

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

Question 8

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 9

Wood Specialties Company produces wall shelves, bookends, and shadow boxes. It is necessary to plan the production schedule for next week. The wall shelves, bookends, and shadow boxes are made of oak, of which the company has 600 board feet. A wall shelf requires 4 board feet, bookends require 2 board feet, and a shadow box requires 3 board feet. The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes, bookends require 15 minutes, and a shadow box requires 15 minutes. The power saw is expected to be available for 36 hours next week. After cutting, the pieces of work in process are hand finished in the finishing department, which consists of 4 skilled and experienced craftsmen, each of whom can complete any of the products. A wall shelf requires 60 minutes of finishing, bookends require 30 minutes, and a shadow box requires 90 minutes. The finishing department is expected to operate for 40 hours next week. Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95.
(A) Is this a problem in maximization or minimization?
(B) What are the decision variables? Suggest symbols for them.
(C) What is the objective function?
(D) What are the constraints?

Accepted Answer

(A) Since the problem contains informati

Question 10

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)?

Accepted Answer

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 
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 11

Nonzero slack or surplus is associated with a binding constraint.

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

Question 14

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

Accepted Answer

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 
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 15

When we use less of a resource than was available, in linear programming that resource would be called non-__________.

Accepted Answer

A)  binding 
B)  feasible 
C)  reduced cost 
D)  linear 
E)  enumerated 
A)  binding 
B)  feasible 
C)  reduced cost 
D)  linear 
E)  enumerated

Question 16

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?

Accepted Answer

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

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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?

Accepted Answer

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

Question 19

Consider the following linear programming problem: Maximize $Z = \$ 15 X + \$ 20 y$
$\begin{array} { c } 
\text{Subject to:}&8 x + 5 y \leq 40 \
&4 x + y \geq 4
\end{array}$ Solve the values of x and y that will maximize revenue. What revenue will result?

Accepted Answer

x = 0, y =

Question 20

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

Accepted Answer

A) True 
 B)False

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

LP problems must have a single goal or objective specified.

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

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

Nonzero slack or surplus is associated with a binding constraint.

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

For the following constraints, which point is in the feasible solution space of this maximization problem? 14x+6y \leq42 x-y \leq3

When we use less of a resource than was available, in linear programming that resource would be called non-__________.

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

Consider the following linear programming problem: Maximize $Z = \$ 15 X + \$ 20 y$ Subject to: 8x+5y\leq40 4x+y\geq4 Solve the values of x and y that will maximize revenue. What revenue will result?

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

Introduction to Operations Management

Competitiveness, Strategy, and Productivity

Forecasting

Product and Service Design

Extension: Reliability

Strategic Capacity Planning for Products and Services

Extension: Decision Theory

Process Selection and Facility Layout

Work Design and Measurement

Extension: Learning Curves

Location Planning and Analysis

Extension: The Transportation Model

Management of Quality

Quality Control

Extension: Acceptance Sampling

Aggregate Planning and Master Scheduling

MRP and ERP

Inventory Management

Jit and Lean Operations

Extension: Maintenance

Supply Chain Management

Scheduling

Project Management

Management of Waiting Lines

Filters

Exam 19: Linear Programming

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

LP problems must have a single goal or objective specified.

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

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

Nonzero slack or surplus is associated with a binding constraint.

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

For the following constraints, which point is in the feasible solution space of this maximization problem? 14x+6y \leq42 x-y \leq3

When we use less of a resource than was available, in linear programming that resource would be called non-__________.

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

Consider the following linear programming problem: Maximize Z=$15X+$20yZ = \$ 15 X + \$ 20 yZ=$15X+$20y Subject to: 8x+5y\leq40 4x+y\geq4 Solve the values of x and y that will maximize revenue. What revenue will result?

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

Introduction to Operations Management

Competitiveness, Strategy, and Productivity

Forecasting

Product and Service Design

Extension: Reliability

Strategic Capacity Planning for Products and Services

Extension: Decision Theory

Process Selection and Facility Layout

Work Design and Measurement

Extension: Learning Curves

Location Planning and Analysis

Extension: The Transportation Model

Management of Quality

Quality Control

Extension: Acceptance Sampling

Aggregate Planning and Master Scheduling

MRP and ERP

Inventory Management

Jit and Lean Operations

Extension: Maintenance

Supply Chain Management

Scheduling

Project Management

Management of Waiting Lines

Filters

Consider the following linear programming problem: Maximize $Z = \$ 15 X + \$ 20 y$ Subject to: 8x+5y\leq40 4x+y\geq4 Solve the values of x and y that will maximize revenue. What revenue will result?