A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.
| Product |
Material #1 (pounds) |
Material #2 (pounds) |
Labor Hours |
| A |
3 |
2 |
4 |
| B |
1 |
4 |
2 |
| C |
5 |
0 |
3.5 |
Courtesy of Terry Klinker
Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for $67 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material #1; 400 pounds of material #2; and 200 hours of labor. Moreover, there is a standing order of 10 units of product C each week.
Linear Programming Formulation
Maximize: 10A + 10B + 10C
Subject to:
3A + 1B + 5C = 300 (constraint #1)
2A + 4B = 400 (constraint #2)
4A + 2B + 3.5C = 200 (constraint #3)
C = 10 (constraint #4)
All decision variables > 0
Sensitivity Report
Adjustable Cells
| Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease |
| $B$4 |
Optimal Values: A |
0 |
-10 |
10 |
10 |
1E+30 |
| $C$4 |
Optimal Values: B |
82.5 |
0 |
10 |
1E+30 |
4.285 |
| $D$4 |
Optimal Values: C |
10 |
0 |
10 |
7.5 |
1E+30 |
Courtesy of Terry Klinker
Constraints
| Cell | Name | Final Value | Shadow Price | Constraint R.H.S. Side | Allowable Increase | Allowable Decrease |
| $E$7 |
Constraint 1 |
132.5 |
0 |
300 |
1E+30 |
167.5 |
| $E$8 |
Constraint 2 |
330 |
0 |
400 |
1E+30 |
70 |
| $E$9 |
Constraint 3 |
200 |
5 |
200 |
35 |
165 |
| $E$10 |
Constraint 4 |
10 |
-7.5 |
10 |
47.142 |
10 |
Courtesy of Terry Klinker
1.The production manager adds an addition laborer, increasing labor hours by 40. What impact will this have on the current objective function value?
2.Suppose that the production manager has an additional 100 pounds of material 1. What impact will this have on the current optimal objective function value?