A factory produces four products. Each product needs to be processed successivel

Question

A factory produces four products. Each product needs to be processed successively on two machines – machine A and then machine B. The processing times in hours per unit of the products on the two machines are shown in the following table.

The total cost of producing one unit of each product is based directly on the machine time. Assume that the costs per hour for machines A and B are $20 and $10, respectively. The total number of hours available each month is 500 for machine A and 380 for machine B. The unit sales prices for products 1, 2, 3, and 4 are $130, $140, $110, and $90, respectively. The factory wants to determine the monthly production quantity of each product so that the total profit can be maximized. Formulate the problem as a linear programming model and solve it using Excel solver (print and attach your Excel output).

processing times (hours) per unit of    machine product 1 product 2 product 3 product 4 a 2 3 4 2 b 3 2 1 2

Explanation / Answer

Let number of units produced of Product1 , Product2 , Product3 and Product4 be x1 , x2 , x3 and x4

Profit , P = 130x1 + 140x2 + 110x3 + 90x4 - 20( 2x1 + 3x2 + 4x3 + 2x4 ) - 10( 3x1 + 2x2 + x3 + 2x4 )

P = 60x1 + 60x2 + 20x3 + 30x4

Constraint Equations

2x1 + 3x2 + 4x3 + 2x4 500

3x1 + 2x2 + x3 + 2x4 380

x1 , x2 , x3 , x4 0

By Excel Solving the Output comes out to be

x1 = 28 , x2 = 140 , x3 = 0 and x4 = 0

which makes Profit , P = 60( 28 ) + 60( 148 ) + 20( 0 ) + 30( 0 ) = 10560

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