(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 $12, 9, and 7 respectively, formulate a linear mixed integer program to determine the optimal production schedule that will maximize the total profit.
TABLE 5.16 Data for Exercise 5.7
Product A Product B Product C
Production (Units) Unit Cost ($) 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.