Question 1

Binding constraints have

Accepted Answer

A) zero slack. 
B) negative slack. 
C) positive slack. 
D) surplus resources. 
A) zero slack. 
B) negative slack. 
C) positive slack. 
D) surplus resources.

Question 2

The following questions are based on the problem below and accompanying Risk Solver Platform (RSP) sensitivity report.
Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
   The following is the LP model for this logistics problem.
    
-Refer to Exhibit 4.1. Are there alternate optimal solutions to this problem?

Accepted Answer

Cannot tell because we cannot rule out d

Question 3

When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero it indicates (in the absence of degeneracy) that

Accepted Answer

A) the problem is infeasible. 
B) alternate optimal solutions exist. 
C) there is only one optimal solution. 
D) no optimal solution can be found. 
A) the problem is infeasible. 
B) alternate optimal solutions exist. 
C) there is only one optimal solution. 
D) no optimal solution can be found.

Question 4

What is the value of the slack variable in the following constraint when X1 and X2 are nonbasic and only non-negativity is used as simple bounds? X1 + X2 + S1 = 100

Accepted Answer

A) 0 
B) 50 
C) 100 
D) can't be determined from the given information 
A) 0 
B) 50 
C) 100 
D) can't be determined from the given information

Question 5

Risk Solver Platform (RSP) provides all of the following reports except

Accepted Answer

A) Answer 
B) Sensitivity 
C) Cost performance 
D) Limits 
A) Answer 
B) Sensitivity 
C) Cost performance 
D) Limits

Question 6

When performing sensitivity analysis, which of the following assumptions must apply?

Accepted Answer

A) All other coefficients remain constant. 
B) Only right hand side changes really mean anything. 
C) The X1 variable change is the most important. 
D) The non-negativity assumption can be relaxed 
A) All other coefficients remain constant. 
B) Only right hand side changes really mean anything. 
C) The X1 variable change is the most important. 
D) The non-negativity assumption can be relaxed

Question 7

When a solution is degenerate the reduced costs for the changing cells

Accepted Answer

A) is always equal to zero. 
B) may not be unique. 
C) may be set to any value the manager needs. 
D) is equal to infinity. 
A) is always equal to zero. 
B) may not be unique. 
C) may be set to any value the manager needs. 
D) is equal to infinity.

Question 8

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Accepted Answer

A) an alternate optimal solution exists. 
B) an error in formulation has been made. 
C) the right hand sides should be increased. 
D) the objective function needs new coefficients. 
A) an alternate optimal solution exists. 
B) an error in formulation has been made. 
C) the right hand sides should be increased. 
D) the objective function needs new coefficients.

Question 9

Given the following Risk Solver Platform (RSP) sensitivity output how much does the objective function coefficient for X2 have to increase before it enters the optimal solution at a strictly positive value?

Accepted Answer

Question 10

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem.
   Suppose the farmer can purchase more fertilizer for $2.50 per pound, should he purchase it and how much can he buy and still be sure of the value of the additional fertilizer? Base your response on the following Risk Solver Platform (RSP) sensitivity output.

Accepted Answer

Yes, because the cost of $2.50

Question 11

When a manager considers the effect of changes in an LP model's coefficients he/she is performing

Accepted Answer

A) a random analysis. 
B) a coefficient analysis. 
C) a sensitivity analysis. 
D) a qualitative analysis. 
A) a random analysis. 
B) a coefficient analysis. 
C) a sensitivity analysis. 
D) a qualitative analysis.

Question 12

Given the following Risk Solver Platform (RSP) sensitivity output what range of values can the objective function coefficient for variable X1 assume without changing the optimal solution?

Accepted Answer

The answer of Given the following Risk Solver Platform (RSP)...

Question 13

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

Accepted Answer

A) Status report 
B) Slack report 
C) Results report 
D) Cell Value report 
A) Status report 
B) Slack report 
C) Results report 
D) Cell Value report

Question 14

The allowable decrease for a constraint is

Accepted Answer

A) how many more units of resource to purchase to maximize profits. 
B) the amount by which the resource can decrease given shadow price. 
C) how much resource to use to get the optimal solution. 
D) the amount by which constraint coefficient can increase without changing the final optimal value. 
A) how many more units of resource to purchase to maximize profits. 
B) the amount by which the resource can decrease given shadow price. 
C) how much resource to use to get the optimal solution. 
D) the amount by which constraint coefficient can increase without changing the final optimal value.

Question 15

The slope of the level curve for the objective function value can be changed by

Accepted Answer

A) increasing the value of the decision variables. 
B) doubling all the coefficients in the objective function. 
C) increasing the right hand sides of constraints. 
D) changing a coefficient in the objective function. 
A) increasing the value of the decision variables. 
B) doubling all the coefficients in the objective function. 
C) increasing the right hand sides of constraints. 
D) changing a coefficient in the objective function.

Question 16

The sensitivity analysis provides information about which of the following:

Accepted Answer

A) the impact of a change to an objective function coefficient. 
B) the impact of a change in a resource level. 
C) the impact of adding simple upper or lower bounds on a decision variable. 
D) all of these. 
A) the impact of a change to an objective function coefficient. 
B) the impact of a change in a resource level. 
C) the impact of adding simple upper or lower bounds on a decision variable. 
D) all of these.

Question 17

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited so at most 8 will be produced.Suppose the company can purchase more varnishing time for $3.00, should it be purchased and how much can be bought before the value of the additional time is uncertain? Base your response on the following Risk Solver Platform (RSP) sensitivity output.
   The LP model for the problem is

Accepted Answer

Yes, because the cost of $3.00

Question 18

The following questions correspond to the problem below and associated Risk Solver Platform (RSP) sensitivity report.
Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations:
   The following LP model allows Robert to maximize his numerical grade.    
-Refer to Exhibit 4.2. Constraint cell F9 corresponds to the constraint, W1 + W2 + W3 + W4 = 1, and has a shadow price of 75. Armed with this information, what can Robert request of his instructor regarding this constraint?

Accepted Answer

Nothing. The constraint has th

Question 19

The following questions are based on the problem below and accompanying Risk Solver Platform (RSP) sensitivity report.
Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
   The following is the LP model for this logistics problem.
    
-Refer to Exhibit 4.1. Of the three percentage of effort constraints, Shipped by Truck, Shipped by Rail, and Shipped by Air, which should be examined for potential cost reduction?

Accepted Answer

The percentage by Truck, Shipp

Question 20

For a minimization problem, if a decision variable's final value is 0, and its reduced cost is negative, which of the following is true?

Accepted Answer

A) Alternate optimal solutions exist. 
B) There is evidence of degeneracy. 
C) No feasible solution was found. 
D) The variable has a non-negativity constraint. 
A) Alternate optimal solutions exist. 
B) There is evidence of degeneracy. 
C) No feasible solution was found. 
D) The variable has a non-negativity constraint.

Binding constraints have

When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero it indicates (in the absence of degeneracy) that

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁+ X₂ + S₁ = 100

Risk Solver Platform (RSP) provides all of the following reports except

When performing sensitivity analysis, which of the following assumptions must apply?

When a solution is degenerate the reduced costs for the changing cells

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Given the following Risk Solver Platform (RSP) sensitivity output how much does the objective function coefficient for X₂ have to increase before it enters the optimal solution at a strictly positive value?

When a manager considers the effect of changes in an LP model's coefficients he/she is performing

Given the following Risk Solver Platform (RSP) sensitivity output what range of values can the objective function coefficient for variable X1 assume without changing the optimal solution?

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

The allowable decrease for a constraint is

The slope of the level curve for the objective function value can be changed by

The sensitivity analysis provides information about which of the following:

For a minimization problem, if a decision variable's final value is 0, and its reduced cost is negative, which of the following is true?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

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Exam 4: Sensitivity Analysis and the Simplex Method

Binding constraints have

When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero it indicates (in the absence of degeneracy) that

What is the value of the slack variable in the following constraint when X1 and X2 are nonbasic and only non-negativity is used as simple bounds? X1 + X2 + S1 = 100

Risk Solver Platform (RSP) provides all of the following reports except

When performing sensitivity analysis, which of the following assumptions must apply?

When a solution is degenerate the reduced costs for the changing cells

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Given the following Risk Solver Platform (RSP) sensitivity output how much does the objective function coefficient for X2 have to increase before it enters the optimal solution at a strictly positive value?

When a manager considers the effect of changes in an LP model's coefficients he/she is performing

Given the following Risk Solver Platform (RSP) sensitivity output what range of values can the objective function coefficient for variable X1 assume without changing the optimal solution?

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

The allowable decrease for a constraint is

The slope of the level curve for the objective function value can be changed by

The sensitivity analysis provides information about which of the following:

For a minimization problem, if a decision variable's final value is 0, and its reduced cost is negative, which of the following is true?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁+ X₂ + S₁ = 100

Given the following Risk Solver Platform (RSP) sensitivity output how much does the objective function coefficient for X₂ have to increase before it enters the optimal solution at a strictly positive value?