A company produces glass products and own 3 plants. The management decides to pr

Question

A company produces glass products and own 3 plants. The management decides to produce two new products and need to decide how much to produce of each one to maximize their profit. Each ton of Product 1 requires 1 hour of production time in Plant 1 and 3 hours in Plant 3 and will generate $3,000 profit. Each ton of Product 2 requires 2 hours of production time in Plant 2 and 2 hours in Plant 3 and will generate $5,000 profit. The production times available per week for each plant are 4, 12 and 18 hours respectively for Plant 1, 2 and 3. Identifies variables, formulate as a LP

Explanation / Answer

Let x and y be the number of tons of product 1 and 2 respectively.

Linear programming statement is to maximize Profit(p) = 3000x + 5000y

Subject to

x <= 4 (Plant 1 constraint)

2y <=12 ( Plant 2 constraint)

3x + 2y <= 18 ( Plant 3 constraint )

Solving this linear programming equation gives the answer as x = 2 , y= 6

Profit = (3000 * 2) + (5000*6) = 36000

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