A firm makes three products, A, B, and C and uses three different machines in the process: W, X, and Y. Weekly demand for products A, B, and C is 300, 250, and 150 units, respectively, while each machine is available 2,400 minutes per week. The flow process, raw material costs and selling prices per unit of product, and machine processing times for each product are below. Find:1). the system constraint, 2). the weekly product mix that provides the highest profit, and 3). the maximum weekly profit that the plant can earn, given the mix in part (2).
Product A:
costs a total of $40 to make and sells for $50
X (1 min) ($15), then W (2 min) ($15), then Y (3 min) ($10)
Product B:
costs a total of $45 to make and sells for $60
W (2 min) ($15), then X (6 min)($20), then Y (5 min) ($10)
Product C:
costs a total of $60 to make and sells for $70
W (5 min) ($30), then Y (4 min) ($20), then X (4 min) ($10)