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126 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

Figure 3.15 The Management Scientist Solution for the GulfGolf Glove Problem

Original
Name Value Final Value
Maximize Total Profit 0 3700

Original
Name Value Final Value
Units produced Regular 0 500
Units produced 0 150
Professional

Name Cell Value Status Slack
Cutting and Sewing 725 Not Binding 175
Hours Used(LHS)
Finishing Hours 300 Binding 0
Used(LHS)
Packaging and shipping 100 Binding 0
Hours Used(LHS)

Adjustable Cells
Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
Units produced Regular 500 0 5 7 1
Units produced 150 0 8 2 4.666666667
Professional
Constraints
Final Shadow Constraint Allowable Allowable
Name Value Price R.H. Side Increase Decrease
Cutting and Sewing 725 0 900 1E+30 175
Hours Used(LHS)
Finishing Hours 300 3 300 100 166.6666667
Used(LHS)
Packaging and shipping 100 28 100 35 25
Hours Used(LHS)

The computer solution of this problem is shown in Figure 3.16.
a. What is the optimal solution, and what is the value of the total annual return?
b. Which constraints are binding? What is your interpretation of these constraints in terms
of the problem?
c. What are the dual prices for the constraints? Interpret each.
d. Would it be beneficial to increase the maximum amount invested in United Oil? Why or
why not?
11 Refer to Figure 3.16, which shows the computer solution of Problem 10.
a. Howmuch would theestimated per-share return for United Oilhaveto increase
before it would be beneficial to increase the investment in this stock?
b. How much would the estimated per-share return for Huber Steel have to decrease
before it would be beneficial to reduce the investment in this stock?
c. How much would the total annual return be reduced if the United Oil maximum were
reduced to 900 shares?

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