Two products A and B are to be machined on three machine tools P, Q and R. Product A takes 10 hrs on machine P, 6 hrs on machine Q and 5 hrs on machine R. The product B takes 7.5 hrs on machine P, 9 hrs on machining Q and 13 hrs on machine R. The machining time available on these machine tools P, Q, R are respectively 75 hrs, 54 hrs and 65 hrs per week. The producer contemplates profit of Rs. 60 per product A, and Rs. 70 per product B. Formulate LP model for the above problem and show the feasible region graphically/geometrically. What are the basic feasible solutions to the above problem?
Estimate graphically/geometrically the optimum product mix for maximizing the profit. Explain why one of the vertices of the feasible region becomes the optimum solution point. (Note: Graph sheet need not be used).