Consider the following linear program.Max 3A + 2Bs.t.1A1B ≤ 103A + 1B ≤ 221A + 2B ≤ 18A, B ≥ 0(a) Use the graphical solution procedure to find the optimal solution.What is the value of the objective function at the optimal solution?at (A, B) =(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution.Does the optimal solution change?The extreme point(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure tofind the new optimal solution.Does the optimal solution change?The extreme pointVariable(d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.Objective Allowable AllowableCoefficient Increase DecreaseAB---Select--- optimal. The value of the objective function becomes3.000002.00000---Select--- optimal. The value of the objective function becomes3.000001.000001.000001.00000 Use this objective coefficient range information to answer parts (b) and (c).The objective coefficient range for variable A isto---Select--- change. The objective coefficient range for variable B isoptimal solution ---Select--- ✓ change.Since the change in part (b) is ---Select--- this range, we know the optimal solutionSince the change in part (c) is ---Select--- this range, we know theto

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(a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? at (A, B) = (b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point ---Select--- optimal. The value of the objective function becomes (c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point ---Select--- optimal. The value of the objective function becomes

(a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? at (A, B) = (b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point ---Select--- optimal. The value of the objective function becomes (c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point ---Select--- optimal. The value of the objective function becomes

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

Consider the following linear program.
Max 3A + 2B
s.t.
1A
1B ≤ 10
3A + 1B ≤ 22
1A + 2B ≤ 18
A, B ≥ 0
(a) Use the graphical solution procedure to find the optimal solution.
What is the value of the objective function at the optimal solution?
at (A, B) =
(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution.
Does the optimal solution change?
The extreme point
(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to
find the new optimal solution.
Does the optimal solution change?
The extreme point
Variable
(d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.
Objective Allowable Allowable
Coefficient Increase Decrease
A
B
---Select--- optimal. The value of the objective function becomes
3.00000
2.00000
---Select--- optimal. The value of the objective function becomes
3.00000
1.00000
1.00000
1.00000

Use this objective coefficient range information to answer parts (b) and (c).
The objective coefficient range for variable A is
to
---Select--- change. The objective coefficient range for variable B is
optimal solution ---Select--- ✓ change.
Since the change in part (b) is ---Select--- this range, we know the optimal solution
Since the change in part (c) is ---Select--- this range, we know the
to

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