Question 1

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

Accepted Answer

A) True 
 B)False

Question 2

What is the usefulness of a shadow price (or dual value)?

Accepted Answer

Shadow prices and dual values are found

Question 3

The Queen City Nursery manufactures bags of potting soil from compost and topsoil. Each cubic foot of compost costs 12 cents and contains 4 pounds of sand, 3 pounds of clay, and 5 pounds of humus. Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand, 6 pounds of clay, and 12 pounds of humus. Each bag of potting soil must contain at least 12 pounds of sand, 12 pounds of clay, and 10 pounds of humus. Explain how this problem meets the conditions of a linear programming problem. Plot the constraints and identify the feasible region. Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag. Identify the lowest cost possible.

Accepted Answer

The problem formulation appears in the s

Question 4

Lost Maples Winery makes three varieties of contemporary Texas Hill Country wines: Austin Formation (a fine red), Ste. Genevieve (a table white), and Los Alamos (a hearty pink Zinfandel). The raw materials, labor, and contribution per case of each of these wines is summarized below.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \begin{array} { c } 
\text { Grapes } \
\text { Variety A } \
\text { bushels }
\end{array} & \begin{array} { c } 
\text { Grapes } \
\text { Variety B } \
\text { bushels }
\end{array} & \begin{array} { c } 
\text { Sugar } \
\text { pounds }
\end{array} & \begin{array} { c } 
\text { Labor (man- } \
\text { hours) }
\end{array} & \begin{array} { c } 
\text { Contrib. } \
\text { per case }
\end{array} \
\hline \text { Austin Formation } & 4 & 0 & 1 & 3 & \$ 24 \
\hline \text { Ste. Genevieve } & 0 & 4 & 0 & 1 & \$ 28 \
\hline \text { Los Alamos } & 2 & 2 & 2 & 2 & \$ 20 \
\hline
\end{array}$$ 
The winery has 2800 bushels of Variety A grapes, 2040 bushels of Variety B grapes, 800 pounds of sugar, and 1060 man-hours of labor available during the next week. The firm operates to achieve maximum contribution. Refer to the POM for Windows panels showing the solution to this problem.
   
Answer the following questions.
a. For maximum contribution, how much of each wine should be produced?
b. How much contribution will be made by selling the output?
c. Is there any sugar left over?
 If so, how much?
 If not, what is its shadow price (dual value)?
 Explain what this value means to Lost Maples' management.
d. Interpret the meaning of the lower bound to Labor in the Ranging analysis. That is, explain how the solution would change if the amount of labor fell below that lower value.
e. Interpret the meaning of the upper bound to Los Alamos wine in the Ranging analysis.

Accepted Answer

(a) 183 1/3 cases of Austin Formation, 5

Question 5

A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100, plus non-negativity constraints on X and Y. Which of the following statements about its feasible region is true?

Accepted Answer

A)  The points (100, 0) and (0, 25) both lie outside the feasible region. 
B)  The two corner points are (33-1/3, 8-1/3) and (50, 0). 
C)  The graphical origin (0, 0) is not in the feasible region. 
D)  The feasible region is a straight line segment, not an area. 
E)  All of the above are true. 
A)  The points (100, 0) and (0, 25) both lie outside the feasible region. 
B)  The two corner points are (33-1/3, 8-1/3) and (50, 0). 
C)  The graphical origin (0, 0) is not in the feasible region. 
D)  The feasible region is a straight line segment, not an area. 
E)  All of the above are true.

Question 6

Suppose that the shadow price for assembly time is $5/hour. If all assembly hours were used under the initial LP solution and workers normally make $4/hour but can work overtime for $6/hour, what should management do?

Accepted Answer

A)  do not change available hours for assembly time 
B)  decrease available hours for assembly time 
C)  increase available hours for assembly time 
D)  not enough information 
E)  Either A or C will result in larger profits than B. 
A)  do not change available hours for assembly time 
B)  decrease available hours for assembly time 
C)  increase available hours for assembly time 
D)  not enough information 
E)  Either A or C will result in larger profits than B.

Question 7

John's Locomotive Works manufactures a model locomotive. It comes in two versions--a standard (X1), and a deluxe (X2). The standard version generates $250 per locomotive for the standard version, and $350 per locomotive for the deluxe version. One constraint on John's production is labor hours. He only has 40 hours per week for assembly. The standard version requires 250 minutes each, while the deluxe requires 350 minutes. John's milling machine is also a limitation. There are only 20 hours a week available for the milling machine. The standard unit requires 60 minutes, while the deluxe requires 120. Formulate as a linear programming problem, and solve using either the graphical or corner points solution method.

Accepted Answer

The answer of John's Locomotive Works manufactures a model locomotive....

Question 8

What combination of a and b will yield the optimum for this problem?
Maximize $6a + $15b, subject to (1) 4a + 2b < 12 and (2) 5a + 2b < 20 and (3) a, b ≥ 0.

Accepted Answer

A)  a = 0, b = 0 
B)  a = 3, b = 3 
C)  a = 0, b = 6 
D)  a = 6, b = 0 
E)  cannot solve without values for a and b 
A)  a = 0, b = 0 
B)  a = 3, b = 3 
C)  a = 0, b = 6 
D)  a = 6, b = 0 
E)  cannot solve without values for a and b

Question 9

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.

Accepted Answer

A) True 
 B)False

Question 10

The difference between minimization and maximization problems is that

Accepted Answer

A)  minimization problems cannot be solved with the corner-point method 
B)  maximization problems often have unbounded regions 
C)  minimization problems often have unbounded regions 
D)  minimization problems cannot have shadow prices 
E)  None of the above are true. 
A)  minimization problems cannot be solved with the corner-point method 
B)  maximization problems often have unbounded regions 
C)  minimization problems often have unbounded regions 
D)  minimization problems cannot have shadow prices 
E)  None of the above are true.

Question 11

Suppose that a constraint is given by X+Y≤10. If another constraint is given to be 3X+2Y≥15 determine the corners of the feasible solution. If the profit from X is 5 and the profit from Y is 10, determine the maximum profit.

Accepted Answer

Corners are (10,0), (5,0), (0,

Question 12

A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

Accepted Answer

A)  There are four corner points including (50, 0) and (0, 12.5). 
B)  The two corner points are (0, 0) and (50, 12.5). 
C)  The graphical origin (0, 0) is not in the feasible region. 
D)  The feasible region includes all points that satisfy one constraint, the other, or both. 
E)  The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. 
A)  There are four corner points including (50, 0) and (0, 12.5). 
B)  The two corner points are (0, 0) and (50, 12.5). 
C)  The graphical origin (0, 0) is not in the feasible region. 
D)  The feasible region includes all points that satisfy one constraint, the other, or both. 
E)  The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Question 13

In a linear programming problem, what is the relationship between the constraints and the feasible region?
 Explain with reference to a problem with two variables.

Accepted Answer

Each constraint appears on a graph as an

Question 14

What combination of x and y will yield the optimum for this problem?
Maximize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

Accepted Answer

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

Question 15

Which of the following correctly describes all iso-profit lines for an LP maximization problem?

Accepted Answer

A)  They all pass through the origin 
B)  They are all parallel. 
C)  They all pass through the point of maximum profit. 
D)  Each line passes through at least 2 corners. 
E)  All of the above 
A)  They all pass through the origin 
B)  They are all parallel. 
C)  They all pass through the point of maximum profit. 
D)  Each line passes through at least 2 corners. 
E)  All of the above

Question 16

Suppose that a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be X+ 2Y what is the maximum profit the company can earn?

Accepted Answer

A)  $0 
B)  $10 
C)  $15 
D)  $14 
E)  None of the above or Unable to determine 
A)  $0 
B)  $10 
C)  $15 
D)  $14 
E)  None of the above or Unable to determine

Question 17

The __________ is the set of all feasible combinations of the decision variables.

Accepted Answer

The answer of The __________ is the set of all...

Question 18

A stereo mail order center has 8,000 cubic feet available for storage of its private label loudspeakers. The ZAR-3 speakers cost $295 each and require 4 cubic feet of space; the ZAR-2ax speakers cost $110 each and require 3 cubic feet of space; and the ZAR-4 model costs $58 and requires 1 cubic foot of space. The demand for the ZAR-3 is at most 20 units per month. The wholesaler has $100,000 to spend on loudspeakers this month. Each ZAR-3 contributes $105, each ZAR-2ax contributes $50, and each ZAR-4 contributes $28. The objective is to maximize total contribution. Write out the objective and the constraints.

Accepted Answer

The objective is to maximize 105 ZAR-3 +

Question 19

A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest. The four investments available are A, B, C, and D. Investment A will earn 4 percent and has a risk of two "points" per $1,000 invested. B earns 6 percent with 3 risk points; C earns 9 percent with 7 risk points; and D earns 11 percent with a risk of 8. The client has put the following conditions on the investments: A is to be no more than one-half of the total invested. A cannot be less than 20 percent of the total investment. D cannot be less than C. Total risk points must be at or below 1,000.Identify the decision variables of this problem. Write out the objective function and constraints. Do not solve.

Accepted Answer

Maximize 0.04A + 0.06B + 0.09C + 0.11D
S

Question 20

Two methods of conducting sensitivity analysis on solved linear programming problems are __________ and __________.

Accepted Answer

postoptima

Exam 22: Linear Programming

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

What is the usefulness of a shadow price (or dual value)?

A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100, plus non-negativity constraints on X and Y. Which of the following statements about its feasible region is true?

Suppose that the shadow price for assembly time is $5/hour. If all assembly hours were used under the initial LP solution and workers normally make $4/hour but can work overtime for $6/hour, what should management do?

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b, subject to (1) 4a + 2b < 12 and (2) 5a + 2b < 20 and (3) a, b ≥ 0.

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.

The difference between minimization and maximization problems is that

Suppose that a constraint is given by X+Y≤10. If another constraint is given to be 3X+2Y≥15 determine the corners of the feasible solution. If the profit from X is 5 and the profit from Y is 10, determine the maximum profit.

A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

In a linear programming problem, what is the relationship between the constraints and the feasible region? Explain with reference to a problem with two variables.

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

Which of the following correctly describes all iso-profit lines for an LP maximization problem?

Suppose that a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be X+ 2Y what is the maximum profit the company can earn?

The __________ is the set of all feasible combinations of the decision variables.

Two methods of conducting sensitivity analysis on solved linear programming problems are __________ and __________.

Operations and Productivity

Operations Strategy in a Global Environment

Project Management

Forecasting

Design of Goods and Services

Managing Quality

Statistical Process Control

Process Strategy

Capacity and Constraint Management

Location Strategies

Layout Strategies

Human Resources, Job Design, and Work Measurement

Supply-Chain Management

Outsourcing as a Supply-Chain Strategy

Inventory Management

Aggregate Planning

Material Requirements Planning MRP and ERP

Short-Term Scheduling

Just-In-Time and Lean Options

Maintenance and Reliability

Decision-Making Tools

Transportation Models

Waiting-Line Models

Learning Curves

Simulation

Filters

Two methods of conducting sensitivity analysis on solved linear programming problems are and .