2. (10 points) Two suppliers of products are available to supply the needs of four supermarkets. Each supplier can provide 90 units per day. Each supermarket would like to receive 60 units per day. For each unit per day of unmet demand, there is a penalty. At supermarket A, the penalty is P1,000; at supermarket B, the penalty is P1, 100; at supermarket C, the penalty is P1, 150, and at supermarket D, the penalty is P1, 020. The cost of transporting each unit from each reservoir to each city is shown in the table below. From Supplier 1 Supplier 2 To Supermarket A P 350 Supermarket B P 450 P 400 P 350 Supermarket C P 500 Supermarket D P 300 P 40 P 250 a. Define the decision variables. b. Formulate a balanced transportation problem that can be used to minimize the sum of shortage and transport costs. c. Write a linear programming model for this problem but do not solve the LP model.