Consider the LP formulation given below for a typical two product mix problem in which the resources used are Materials, Labor Hours, and storage. Each ton of product-1 requires 2 hours of labor, 4 tons of materials, and 25 cubic meters of storage. A ton of product-2 requires 1 hours of labor, 3 tons of materials, and 30 cubic meters of storage. In every week the firm has 100 Labor Hours, 240 Tons of Materials, and a storage capacity of 2000 cubic meter. The firm makes a profit of $6 thousands per ton on product-1 and $4 thousands per ton on product-2. If the firm wants to maximize the profit, the following is the graph and the LP formulation:

Maximize 6X1 + 4X2

Subject to

2X1 + 1X2

4X1 + 3X2

25X1 + 25X2

X1, X2 > 0

You might use any method including the graph below to solve and analyze the above problem and answer the ten questions (a m) that follow:

What is the value of the shadow price for resource-1? What is the range of feasibility for this shadow price?

L: 4X1 + 3 -20 WmH840 : 51 + 30 = 2000 X1 + V: 0 24 6 8 ' ' 46 1 2 4 5 8 0 2 4 5 4 5 A1 Payoff: 6X Optimal Decisions(x1,x2): ( 0, 0) : X1+ = 10 : X1 + = 240 : X1 + 302 = 200