7. A producer of limestone for agriculture use has 3 limestone quarries which supply 5 regular warehouses. The inventory position of each of the quarries this week is: Quarry 1 2 3 Tons of lime on hand 200 100 150 Transportation costs per ton from each quarry to each of the regional warehouses and the quantities required by each warehouse are shown below: Transport Costs ($) W1 W2 W3 W 4 W5 Q1 5 6 3 Q2 2 3 4 5 4 Q3 2 3 2 3 Requirements (tons ) 20 90 100 70 60 Set up the objective function and constraints required to obtain the shipping schedule for next week, which will minimize the total transportation cost. 8. A menu is being prepared for the Ateneo's Loyola dorms. The objective is to feed the students at the least possible cost, but the diet must have between 1,800 and 3,600 calories. No more than 1,400 calories can be starch, and no fewer than 400 can be protein. The varied diet is to be made of two foods: A & B. Food A costs Ph35 per pound and contains 600 calories, of which 400 are protein and 200 starch. No more than two pounds of food A can be used per resident. Food B costs Ph7 per pound and contains 900 calories, of which 700 are starch and 100 are protein and 100 are fat. 9. A canning factory obtains the tops of its cans from rectangular metal sheets. The dimensions of each sheet are 16 x 40 cm . Two different sizes of tops are needed. The diameter of the smaller size is 8 cm diameter and that of the larger size is 16 cm diameter. A given day's production schedule calls for at least 20,000 of the smaller size and at least 5,000 of the larger size. The problem facing the company is how to cut these tops from the metal sheets so that the fewest number of sheets is used . ( Hint: determine the pattern or ways to cut the 8 cm and the 16 cm tops from the sheet. Calculate the number of sheets to be cut according to each pattern.) 10. A paper mill produces kraft paper in jumbo reels having a standard width of 68 cm and a finxed length. The company's customers, however, order reels having smaller widths and the same fixed length as the jumbo reel. Today's order are 110 reels of 22cm width, 120 reels of 20cm, and 80 reels of 12 cm width. These smaller widths are to be cut from the jumbo reels. The company wants to manufacture today's orders so as to minimize total trim waste . (Hint; Find every possible way to slit a 68 cm jumbo reel into combinations of 22 cm, 20 cm, and 12 cm width reels. Calculate the trim waste for each combination.)