solution

An appliance manufacturer produces three models of microwave ovens: X, Y, and Z. These models require fabrication, assembly, and packaging work; each X uses 12 hours of fabrication, 9 hours of assembly, and 4 hours of packaging. Each Y uses 8 hours of fabrication, 14 hours of assembly, and 3 hours of packaging. Each Z uses 7 hours of fabrication, 16 hours of assembly, and 2 hours of packaging. There are 2800 fabrication hours, 2500 assembly hours, and 500 packaging hours available this week. X, Y, and Z contribute $8, $7, and $6 to the total profit, respectively. The company must produce at least 100 of Y. To find quantities of X, Y, and Z that will maximize the total profit, build a Linear Programming model and solve the LP model using Solver. What is the optimal total profit? Pick the closest number. (Do not impose an integer constraint. X, Y, Z can take non-integer values.)