Question: Gepbab Corporation produces three products at two different plants. The total cost ( in hundreds of dollars ) of producing a unit (Ton) at each plant is shown in the Table below:

For the coming year, each plant has a production capacity of 10,000 units. Based on current customer commitments, Gepbab need to produce 6000 units of Product 1, 8000 units of Product 2, and 5000 units of Product 3. Let

X11 = Number of units of Product 1 produced at Plant 1

X12 = Number of units of Product 1 produced at Plant 2

X21 = Number of units of Product 2 produced at Plant 1

X22 = Number of units of Product 2 produced at Plant 2

X31 = Number of units of Product 3 produced at Plant 1

X32 = Number of units of Product 3 produced at Plant 2

To minimize the cost of meeting these demands, the following Linear Program should be solved:

Minimize 5X11 + 8X12 + 6X21 + 7X22 + 8X31 + 10X32

S. t.

X11 + X21 + X31 10000 (SUPPLY-1)

X12 + X22 + X32 10000 (SUPPLY-2)

X11 + X12 = 6000 (DEMAND-1)

X21 + X22 = 8000 (DEMAND-2)

X31 + X32 = 5000 (DEMAND-3)

All Variables 0

Using attached SOLVER output, answer the following questions:

1. What is the optimal production plan and the corresponding cost?
2. If it cost only 6 (hundred dollars) to produce a unit of Product 1 at Plant 2, would you still use the production plan of part (a)? Discuss why or why not.
3. For the original problem, by how much the total cost will decrease if Plant 1 had a capacity of 11000 units?
4. Interpret the shadow price of 10 for the DEM-3 (demand of Product-3) constraint? Based on your answer, if PRODUCT-3 sells for $975/unit, will you consider funding a marketing campaign to increase the demand for PRODUCT-3? Discuss why or why not? (Note: Keep in mind that unit of cost in this model is hundreds of dollars).
5. 
   A new customer is willing to purchase 1000 units of PRODUCT 1. What is the minimum you will charge the customer for this order?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document