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Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 52P

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Question

Consider the following linear programming problem, which maximizes profit for two products:
regular (R) and super (S):
MAX 5R + 75S
s.t.
1.2 R+ 1.6 S ≤ 600 assembly (hours)
0.8 R + 0.5 S ≤ 300
paint (hours)
0.16 R+ 0.4 S ≤ 100 inspection (hours)
R, S >= 0
See the sensitivity report provided below:
Variable Cells
Cell
$C$28 Regular-R
$C$29 Super-S
Constraints
Name
Cell
SFS6 assembly (hours)
SFS7 paint (hours)
$F$8 inspection (hours)
Name
Final Reduced Objective Allowable Allowable
Cost Coefficient Increase Decrease
Value
0
250
-25
0
400
125
100
5
25
75 1E+30
Final Shadow Constraint Allowable Allowable
Value Price R.H. Side Increase Decrease
0
0
187.5
1E+30
62.5
600 1E+30
300 1E+30
100
50
200
175
100
The upper limit of the regular product (R) objective function coefficient (profit of R) is

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If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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