Example 3 An auto company manufactures cars and trucks. Each vehicle must be pro

Question

Example 3 An auto company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, 40 per day could be painted. If the paint shop were only painting cars, 60 per day could be painted. If the body shop were only producing cars, it could process 50 per day. If the body shop were o producing trucks, it could process 50 per day. Each truck contributes $300 to profit, and each car contributes $200 to profit. Use linear programming to determine a daily production schedule that will maximize the company's profit. nly

Explanation / Answer

LET X1 BE TRUCK PER DAY, X2 BE CAR PER DAY

Subject to tis,

1/40X1+1/60X2<=1

1/50X1+1/50X2<=1

X1, X2 >=0

Maximisation function will be,

Max Z = 300X1 + 200 X2

After solving the equation grapically,

Max Z (1,1) comes te opyimal solution which means the optimum daily schedule which maximises the daily production will be,

Max Z = 200 * 1 + 300 * 1 = 500 per day.  

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