## Mineral Mining Company sends one truckload of iron and copper ore daily from the mine tothe…

Mineral Mining Company sends one truckload of iron and copper ore daily from the mine to the processing plant. The truck has a weight capacity of 10 tons and a volume capacity of 1200 cubic feet. Each pound of iron ore takes up 0.04 cubic feet of space and yields a net profit of $0.30 when processed. Each pound of copper ore uses 0.08 cubic feet of space and provides $0.50 of net profit. The following LP model is proposed, where I is the number of pounds of iron ore to load on the truck and C is number of pounds of copper ore to load on the truck: Maximize 0.3 I + 0.5 C Subject to I + C < 20000 0.04 I + 0.08 C < 1200 I , C > 0 a. Solve the problem graphically. Explain the optimal solution and objective function value in the context of the problem. b. Graphically and algebraically determine the sensitivity range of each objective function coefficient at the optimal solution of the linear program in Problem 5. Explain the meaning of each range in the context of the problem. c.For each constraint that holds with equality at the optimal solution of the linear program in the given problem, perform the following: – Graphically and algebraically determine the sensitivity range of the right-hand-side value. – Calculate the shadow price associated with each sensitivity range found in part (a). Explain the meaning of the shadow price in the context of the problem. For the problem of Mineral Mining Company in Problem 5, management is considering leasing one of the following two new trucks to replace the existing one: TRUCK WEIGHT VOLUME ADDITIONAL TYPE CAPACITY(lb) CAPACITY (ft)3 COST ($/day) Tr 22/12 22,000 1,200 100 Tr 20/13 20,000 1,300 150 Should the company replace the old truck? And, if so, with which one of the new trucks should the company replace? Explain. (Use results from the last problem)

1. Mineral Mining Company sends one truckload of iron and copper ore daily from the mine to the processing plant. The truck has a weight capacity of 10 tons and a volume capacity of 1200 cubic feet. Each pound of iron ore takes up 0.04 cubic feet of space and yields a net profit of $0.30 when processed. Each pound of copper ore uses 0.08 cubic feet of space and provides $0.50 of net profit. The following LP model is proposed, where I is the number of pounds of iron ore to load on the truck and C is number of pounds of copper ore to load on the truck:

Maximize 0.3 I + 0.5 C

Subject to

I + C 0

Solve the problem graphically. Explain the optimal solution and objective function value in the context of the problem. (7 points)

b. Graphically and algebraically determine the sensitivity range of each objective function coefficient at the optimal solution of the linear program in Problem 5. Explain the meaning of each range in the context of the problem. (6 points)

For each constraint that holds with equality at the optimal solution of the linear program in Problem 1, perform the following:

c. Graphically and algebraically determine the sensitivity range of the right-hand-side value. (4 points)

d. Calculate the shadow price associated with each sensitivity range found in part (c). Explain the meaning of the shadow price in the context of the problem. (6 points)

e. For the problem of Mineral Mining Company in Problem 1, management is considering leasing one of the following two new trucks to replace the existing one:

Truck Type

Weight Capacity (lb)

Volume Capacity (ft)^3

Additional Cost ($/day)

Tr 22/12

22000

1200

100

Tr 20/13

20000

1300

150

Should the company replace the old truck? And, if so, with which one of the new trucks should the company replace? Explain. (Use results from problem c and d) (5 points)