Classical sensitivity evaluation offers no information around changes resulting from a change in the coefficient of avariable in a constraint.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Changes in constraint coefficients

The lessened expense for a positive decision variable is 0.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Reduced cost

When the right-hand sides of two constraints are each raised by one unit, the objective feature worth will certainly bereadjusted by the amount of the constraints" dual prices.a. True

b. Fals e

ANSWER: False

POINTS: 1

TOPICS: Simultaneous changes

If the array of feasibility shows that the original amount of a source, which was 20, ca rise by 5, then theamount of the resource can increase to 25.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Range of feasibility

The 100% Rule does not indicate that the optimal solution will certainly necessarily change if the portion exceeds 100%.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Simultaneous

changes

For any type of constraint, either its slack/surplus value have to be zero or its dual price need to be zero.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Dual price

A negative dual price suggests that raising the right-hand also side of the linked constraint would be detripsychological tothe objective.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Dual price

In order to tell the affect of a adjust in a constraint coefficient, the adjust must be made and also then the model resolved.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Changes in constraint coefficients

Decreasing the objective attribute coeffective of a variable to its lower limit will produce a revised trouble that isboundless.a. True

b. Fals e

ANSWER: False

POINTS: 1

TOPICS: Range of optimality

The dual price for a portion constraint offers a straight answer to inquiries about the impact of increases ordecreases in that percentage.a. True

b. False

ANSWER: False

POINTS: 1

TOPICS: Dual

output

Any change to the objective feature coeffective of a variable that is positive in the optimal solution will change theoptimal solution.a. True

b. Fals e

ANSWER: False

POINTS: 1

TOPICS: Range of optimality

Relevant costs should be reflected in the objective attribute, however sunk expenses must not.a. True

b. False

ANSWER: True

POINTS: 1

TOPICS: Cautionary note on the interpretation of dual prices

If the selection of feasibility for b 1 is in between 16 and 37, then if b 1 = 22 the optimal solution will not adjust from theoriginal optimal solution.a. True

b. Fals e

ANSWER: False

POINTS: 1

TOPICS: Right-hand sides

The 100 percent ascendancy have the right to be used to alters in both objective feature coefficients and right-hand sides at the sametime.a. True

b. False

ANSWER: False

POINTS: 1

TOPICS: Simultaneous changes

If the dual price for the right-hand also side of a ≤ constraint is zero, tright here is no top limit on its range of feasibility.a. True

b. Fals e

ANSWER: True

POINTS: 1

TOPICS: Right-hand sides

Multiple Choice

To fix a linear programming problem through thousands of variables and constraintsa. a personal computer system deserve to be offered.

You are watching: Sensitivity analysis information in computer output is based on the assumption of

b. a mainstructure computer is forced.

c. the trouble must be partitioned right into subparts.

d. unique software would certainly have to be occurred.

ANSWER: a

POINTS: 1

TOPICS: Computer solution

A negative dual price for a constraint in a minimization difficulty meansa. as the right-hand side boosts, the objective attribute value will certainly increase.

b. as the right-hand also side decreases, the objective attribute worth will boost.

c. as the right-hand side boosts, the objective function worth will certainly decrease.

d. as the right-hand side decreases, the objective feature worth willdecrease.

ANSWER: a

POINTS: 1

TOPICS: Dual price

If a decision variable is not positive in the optimal solution, its decreased cost isa. what its objective feature worth would must be before it can end up being positive.

b. the amount its objective function value would certainly need to improve prior to it could becomepositive.c. zero.

d. its dual price.

ANSWER: b

POINTS: 1

TOPICS: Reduced cost

A constraint via a positive slack valuea. will have actually a positive dual price.

b. will have actually a negative dual price.

c. will have actually a dual price of zero.

d. has actually no constraints for its dual price.

ANSWER: c

POINTS: 1

TOPICS: Slack and dual

price

A section of output from The Management Scientist is shown here.

Variable Lower Limit Current Value Upper Limit1 60 100 120

What will certainly happen to the solution if the objective function coefficient for variable 1 decreases by 20? a. Nothing. The values of the decision variables, the dual prices, and the objective feature will all reprimary the exact same.

b.The value of the objective feature will certainly change, yet the values of the decision variables and also the dual prices will remajor the same.

c. The very same decision variables will be positive, yet their values, the objective feature value, and also the dual prices will readjust. d.The difficulty will must be refixed to find the brand-new optimal solution and dual price.

ANSWER: b

POINTS: 1

TOPICS: Range of optimality

A area of output from The Management Scientist is presented here.

Constraint Lower Limit Current Value Upper Limit2 240 300 420

What will certainly take place if the right-hand-side for constraint 2 boosts by 200? a. Nopoint. The values of the decision variables, the dual prices, and also the objective function will all remain the exact same.

b.The worth of the objective attribute will change, but the worths of the decision variables and the dual prices will certainly remain the exact same.

c. The exact same decision variables will certainly be positive, but their worths, the objective function worth, and the dual prices will change.

d.The difficulty will must be readdressed to uncover the new optimal solution and dual price.

ANSWER: d

POINTS: 1

TOPICS: Range of feasibility

The amount the objective attribute coefficient of a decision variable would certainly have to boost before that variable wouldhave actually a positive value in the solution is thea. dual price.

b. surplusvariable.

c. lessened expense.

d. top limit.

ANSWER: c

POINTS: 1

TOPICS: Interpretation of computer output

The dual price procedures, per unit increase in the appropriate hand also side of the constraint,a. the boost in the worth of the optimal solution.

b. the decrease in the value of the optimal solution.

c. the advancement in the value of the optimalsolution.

d. the change in the worth of the optimal solution.

ANSWER: d

POINTS: 1

TOPICS: Interpretation of computer system output

Sensitivity analysis indevelopment in computer output is based upon the assumption ofa. no coeffective transforms.

b. one coeffective alters.

c. two coefficientsreadjust.

d. all coefficients adjust.

ANSWER: b

POINTS: 1

TOPICS: Simultaneous changes

When the cost of a resource is sunk, then the dual price have the right to be taken as thea. minimum amount the firm must be willing to pay for one additional unit of theresource.

b. maximum amount the firm have to be willing to pay for one added unit of thereresource.

c. minimum amount the firm must be willing to pay for multiple additional devices of thereresource.

d. maximum amount the firm must be willing to pay for multiple additional units of the resource.

ANSWER: b

POINTS: 1

TOPICS: Dual price

Which of the adhering to is not a question answered by standard sensitivity analysis information?a. If the right-hand side value of a constraint alters, will certainly the objective attribute valuechange?b.Over what selection deserve to a constraint"s right-hand side worth without the constraint"s dualprice perhaps changing?

c. By exactly how much will certainly the objective feature value change if the right-hand side value of aconstraint alters past the array of feasibility?

d.By exactly how much will certainly the objective function worth adjust if a decision variable"scoreliable in the objective feature alters within the variety of optimality?

ANSWER: c

POINTS: 1

a. will constantly be 0.

c. will certainly be 0 in a maximization trouble.

d. will constantly equal 0.

ANSWER: b

POINTS: 1

TOPICS: Dual price

Subjective Brief Answer

In a direct programming trouble, the binding constraints for the optimal solution are

5X + 3Y ≤ 302X + 5Y ≤ 20

a. Fill in the blanks in the adhering to sentence:

As long as the slope of the objective attribute continues to be in between ___ and also ___, the existing optimal solution point will certainly remajor optimal.b. Which of these objective functions will cause the exact same optimal solution?

1) 2X + 1Y 2) 7X + 8Y 3) 80X + 60Y 4) 25X + 35YANSWER: a. −5/3 and also −2/ b. Objective functions 2), 3), and also 4)

POINTS: 1

TOPICS: Graphical sensitivity analysis

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.

Max 2x 1 + x 2

s.t. 4x 1 + 1x 2 ≤ 400

4x 1 + 3x 2 ≤ 600

1x 1 + 2x 2 ≤ 300

x 1 , x 2 ≥ 0

a. Over what variety have the right to the coefficient of x 1 differ before the current solution is no longer

optimal?b. Over what array deserve to the coefficient of x 2 vary prior to the existing solution is no longeroptimal?c. Compute the dual prices for the 3 constraints.ANSWER: a. 1.33 ≤ c 1 ≤ 4b. .5 ≤ c 2 ≤ 1.c. Dual prices are .25, .25, 0

POINTS: 1

TOPICS: Graphical sensitivity analysis

The binding constraints for this trouble are the initially and also second.

Min x 1 + 2x 2

s.t. x 1 + x 2 ≥ 300

2x 1 + x 2 ≥ 400

2x 1 + 5x 2 ≤ 750

x 1 , x 2 ≥ 0

a. Keeping c 2 solved at 2, over what array deserve to c 1 differ before tright here is a adjust in the optimal solution point?

b. Keeping c 1 addressed at 1, over what selection have the right to c 2 vary before tright here is a readjust in the optimal solution point?

c. If the objective function becomes Min 1.5x 1 + 2x 2 , what will certainly be the optimal worths of x 1 , x 2 , and also the objective function?

d. If the objective feature becomes Min 7x 1 + 6x 2 , what constraints will be binding?e. Find the dual price for each constraint in the original problem.ANSWER: a. .8 ≤ c 1 ≤ 2 b. 1 ≤ c 2 ≤ 2. c. x 1 = 250, x 2 = 50, z = 475 d. Constraints 1 and 2 will be binding. e. Dual prices are .33, 0, .33 (The first and also third values are negative.)

POINTS: 1

TOPICS: Graphical sensitivity analysis

Excel"s Solver tool has been provided in the spreadsheet below to fix a straight programming difficulty via amaximization objective attribute and also all ≤ constraints.

Input Section

Objective Function CoefficientsX Y4 6

Constraints Avail.#1 3 5 60#2 3 2 48#3 1 1 20

Output Section

Variables 13.333333 4Profit 53.333333 24 77.

Constraint Usage Slack#1 60 1.789E-#2 48 -2.69E-#3 17.333333 2.

0

POINTS: 1

TOPICS: Spreadsheet solution of LPs

Use the spreadsheet and Solver sensitivity report to answer these questions.a. What is the cell formula for B12?b. What is the cell formula for C12?c. What is the cell formula for D12?d. What is the cell formula for B15?e. What is the cell formula for B16?f. What is the cell formula for B17?

g. What is the optimal value for x 1?

h. What is the optimal worth for x 2?i. Would you pay $.50 each for up to 60 more systems of resource 1?

j. Is it feasible to number the brand-new objective attribute worth if the profit on product 1 increases by a dollar, or carry out you need to rerun Solver?

A B C D E 1 2 Input Indevelopment 3 Var. 1 Var. 2 (type) Avail. 4 Constraint 1 2 5 12 7 8 Profit 5 4 910 Output Information11 Variables12 Profit = Total1314 Resources Used Slack/Surplus15 Constraint 116 Constraint 217 Constraint 31819

SensitivityReport

Changing Cells

Final Reduced Objective Allowable AllowableCell Name Value Cost Coeffective Increase Decrease

Constraints

Final Shadow Constraint Allowable AllowableCell Name Value Price R.H. Side Increase Decrease

$B$

ANSWER

: a. =B8B b. =C8C c. =B12+C d. =B4B11+C4C e. =B5B11+C5C f. =B6B11+C6C g. 8. h. 4. i. yes j. no

POINTS: 1

TOPICS: Spreadsheet solution of LPs

Use the following Management Scientist output to answer the questions.

LINEAR PROGRAMMING PROBLEM

MAX 31X1+35X2+32X

S.T.

1) 3X1+5X2+2X3>2) 6X1+7X2+8X3The following direct programming trouble has been resolved by The Management Scientist. Use the output to answerthe inquiries.

LINEAR PROGRAMMING PROBLEM

MAX 25X1+30X2+15X

S.T.

1) 4X1+5X2+8X3LINDO output is given for the complying with direct programming problem.

MIN 12 X1 + 10 X2 + 9 X

SUBJECT TO2) 5 X1 + 8 X2 + 5 X3 >= 603) 8 X1 + 10 X2 + 5 X3 >= 80

END

LP OPTIMUM FOUND AT STEP 1

OBJECTIVE FUNCTION VALUE

1) 80.

VARIABLE VALUE REDUCED COSTX1 .000000 4.X2 8.000000.X3 .000000 4.

Objective Function Value = 7475.

Variable Value Reduced CostX1 8.000 0.X2 0.000 5.X3 17.000 0.X4 33.000 0.

Constraint Slack/Surplus Dual Price1 0.000 75.2 63.000 0.3 0.000 25.4 0.000 −25.

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper LimitX1 87.500 100.000 No Upper LimitX2 No Lower Limit 120.000 125.X3 125.000 150.000 162.X4 120.000 125.000 150.

RIGHT HAND SIDE RANGES

Use the output to answer the inquiries.

a. How many type of necklaces need to be stocked?b. Now many type of arm bands have to be stocked?c. How many rings must be stocked?d. How many earrings have to be stocked?e. How much area will be left unused?f. How much time will be used?g. By just how a lot will certainly the second marketing restriction be exceeded?h. What is the profit?i. To what value have the right to the profit on necklaces drop before the solution would certainly change?j. By exactly how a lot deserve to the profit on rings increase prior to the solution would certainly change?k. By how a lot deserve to the amount of area decrease prior to tright here is a change in the profit?

l.

You are available the opportunity to acquire more area. The offer is for 15 systems and also the total priceis 1500. What should you do?ANSWER: a. 8b. 0c. 17d. 33e. 0f. 57g. 0h. 7475

i. 87.j 12.k. 0l. Say no. Although 15 devices have the right to be evaluated, their value (1125) is less than the price (1500).

POINTS: 1

TOPICS: Interpretation of Management Scientist output

The decision variables recurrent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective functionrepresents profit. The first three constraints meacertain the intake and availcapability of sources A, B, and C. The fourthconstraint is a minimum requirement for ingredient 3. Use the output to answer these concerns.a. How much of ingredient 1 will certainly be put into the blend?b. How a lot of ingredient 2 will certainly be put into the blend?c. How a lot of ingredient 3 will be put right into the blend?d. How a lot resource A is used?e. How much resource B will certainly be left unused?f. What will certainly the profit be?g. What will certainly occur to the solution if the profit from ingredient 2 drops to 4?h. What will certainly happen to the solution if the profit from ingredient 3 rises by 1?i. What will certainly take place to the solution if the amount of resource C boosts by 2?

j. What will certainly occur to the solution if the minimum necessity for ingredient 3 boosts to 15?

LINEAR PROGRAMMING PROBLEM

MAX 4X1+6X2+7X

S.T.

1) 3X1+2X2+5X3

OPTIMAL SOLUTION

Objective Function Value = 166.

Variable Value Reduced CostX1 0.000 2.X2 16.000 0.X3 10.000 0.

Constraint Slack/Surplus Dual Price1 38.000 0.2 2.000 0.3 0.000 1.4 0.000 −2.

See more: Calculate The Percent Yield Of Asa Synthesized In Part A., Lab #3 And 4: Aspirin Synthesis And Analysis

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper LimitX1 No Lower Limit 4.000 6.X2 4.375 6.000 No Upper LimitX3 No Lower Limit 7.000 9.