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(From Ravindran et al. 1987) A company manufactures three products A, B, and C. Each unit of product A requires 1 hour of engineering service, 10 hours of direct labor, and 3 pounds of material. Producing one unit of product B requires 2 hours of engineering, 4 hours of direct labor, and 2 pounds of material. Each unit of product C requires 1 hour of engineering, 5 hours of direct labor, and 1 pound of material. There are 100 hours of engineering, 700 hours of direct labor, and 400 pounds of materials available. The cost of production is a nonlinear function of the quantity produced as shown in Table 3.6. 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.