A company produces two products A and 8. Each unit of product A requires 1 hour of engineering service and 5 hours of machine time. To produce 1 unit of product B requires 2 hours of engineering and 8 hours of machine time. There are 100 hours of engineering and 400 hours of machine time available. The cost of production is a non-linear function of the quality produced as given in the following table:

The unit selling price of product A is Rs 12 and the unit selling price of product Bis Rs 14. The company would like a production plan which gives the number of units of A and the number of units of 8 to be produced that will maximise profit. Formulate an integer programming model for this problem.

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Product A Production (Units) Unit Cost Production (Rs) (Units) Product B Unit Cost (Rs) 0-50 10 0-40 7 51-100 8 41-100 3