LP Formulation and Solve A company manufactures two types of cars, types 1 and 2

Question

LP Formulation and Solve

A company manufactures two types of cars, types 1 and 2. Each car must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 cars, 900 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 cars, 850 per day could be painted. If the assembly shop were completely devoted to assembling car 1 engines 1650 per day could be assembled, and if the assembly shop were completely devoted to assembling car 2 engines, 1500 per day could be assembled. It is possible, however, to paint both types of cars in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 car contributes $300 to profit, each type 2 car contributes S500. According to the recent sales forecast, Carco has to produce at least 200 type 1 cars each day. The objective is to find a production plan that maximizes the daily profit. Formulate your model mathematically and solve it by using the Excel solver

Explanation / Answer

Hence maximum profit is obtained by 200 type I cars and 661 type II cars.

Car Type I x Type II y Total Painting/day 900 850 Assembly/day 1650 1500 Profit 300 500 300x+500y =z x>=200 Objective is to maximise z = 300x+500y Painting days x/900 + y/850 Assembly days x/1650+ y/1500 Since profit is more for type II, 500, type II should be more If 200 type I cars painted, then no of II cars would be = 7/9 (850) = 661 Similarly type II cars assembled can be (1-200/1650)*1500 = 1318 Hence mix can be (900, 0) (200, 661) Profit for (900,0) 270000 Profit for (200,661) 390500

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