For its weekly operations, XYZ receives raw materials from two sources using large tank truck. Each truckload from Eco Petro Ltd contains 2 tons of Raw Material A and 2 tons of Raw Material B at a cost of $20,000. Each truckload from Clean NRG contains 1 ton of Raw Material A and 3 tons of Raw Material B at a cost of $15,000. XYZ requires at least 8 tons of Raw Material A and at least 12 tons of Raw Material B per week. XYZ is to determine how many truckloads should be purchased per week from each source. Formulate and solve a LP that minimizes the XYZ total costs of acquiring the raw materials.

The problem is formulated as a LP problem as follows:

Min Z = 20,000X1+ 15,000X2

Subject to

2X1+ X2 8

2X1+ 3X2 12

X1, X2 0

Your Task

1. Describe the feasible region.

2. Select two levels of the objective function.

3. What is the direction that improves the objective function value?

4. Find the optimal solution and optimal value.