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.

 

TABLE 5.16

Data for Exercise 5.7

Product A                        Product B                         Product C

Production (Units)	Unit Cost ($)	Â	Production (Units)	Unit Cost ($)	Â	Production (Units)	Unit Cost ($)
0–40	10	Â	0–50	6	Â	0–100	5
41–100	9	Â	51–100	4	Â	over 100	4
101–150	8	Â	over 100	3	Â	Â	Â
over 150	7	Â	Â	Â	Â	Â	Â

Note: If 60 units of A are made, the first 40 units cost $10/unit and the remaining 20 units cost $9/unit.