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4. (25 pts) An engineering company produces two products Pl and P2. Each unit of product P1 requires 2 h of engineering service and 5 h of machining time. One unit of P2 requires 3 h of engineering service and 8 h of machining time. There are 135 h of engineering and 600 h of machining time available. The cost of production is a step function as follows. The selling price for product P1 and P2 is $15 and $12, respectively. Formulate an integer programming model to maximize the total profit. Production (units) Unit cost ($) Product P1 0-40 41-100 0-49 50-100 11 9 10 8 P2