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5.7     (Ravindran et al., 1987) A company manufacturers three products A, B, and C. Each unit of product A requires 1 h of engineering service, 10 h of direct labor, and 3 lb of material. To produce one unit of product B requires 2 h of engineering, 4 h of direct labor, and 2 lb of material. Each unit of product C requires 1 h of engineering, 5 h of direct labor, and    1 lb of material. There are 100 h of engineering, 700 h of direct labor, and 400 lb of materials available. The cost of production is a nonlinear function of the quantity produced as shown in Table 5.16.
Given the unit selling prices of products A, B, and C as $12, 9, and 7 respectively, formulate a linear mixed integer program to determine the optimal production schedule that will maximize the total profit.
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TABLE 5.16
Data for Exercise 5.7
Product AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Product BÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Product C
|
Production (Units) |
Unit Cost ($) |
 |
Production (Units) |
Unit Cost ($) |
 |
Production (Units) |
Unit Cost ($) |
|
0–40 |
10 |
 |
0–50 |
6 |
 |
0–100 |
5 |
|
41–100 |
9 |
 |
51–100 |
4 |
 |
over 100 |
4 |
|
101–150 |
8 |
 |
over 100 |
3 |
 |
 |
 |
|
over 150 |
7 |
 |
 |
 |
 |
 |
 |
Note: If 60 units of A are made, the first 40 units cost $10/unit and the remaining 20 units cost $9/unit.
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