A company is producing three types of liquid products: P1, P2, and P3. The production contract is arranged for the next month and assumes the delivery of 4000 liters of the products to a customer. The customer's specifications prescribe that in the delivery, the ratio of product P2 to product P3 cannot exceed 4:1 (i.e. P2/P3 <= 4/1), and the total amount of P1 and P2 must be at most 60% of the total order. The production cost is highest for product P3, therefore the company wants to send as little of this product as possible.
(a) Formulate a linear programming problem to help the company achieve its objective. [5 marks]
(b) Solve the problem graphically. Show the set of feasible solutions. Are there multiple optimal solutions? Hint: notice that the total amount of the products to be delivered is fixed. [10 marks]
(c) The customer specifications contain two conditions (on the ratio and on the percentage of the products). It was renegotiated that only one of the conditions should be taken into account. Amend your model suggested in the answer to (a) to include the new settings. Explain how you define "big" numbers M.