The A-B-C department of a large company makes three products (A, B and C). The department is preparing for its final run next week, which is just before the annual two-week vacation during which the entire department shuts down. The manager wants to use up existing stocks of the three raw materials used to fabricate A, B, and C.

She had formulated the LP model and obtained the optimal results:

X_{1} = quantity of Product A

X_{2} = quantity of Product B

X_{3} = quantity of Product C

Maximize 12X_{1} + 15X_{2} + 14X_{3}

St 3X_{1} + 5X_{2} + 8X_{3} < 840 pounds (Material 1)

2X_{1} + 3X_{3} < 575 pounds (Material 2)

4X_{1} + 6X_{2} + 4X_{3} < 700 pounds (Material 3)

X_{1}, X_{2}, X_{3} > 0

make sure to show the process

Bring your solution to class on the due date.

1. If B’s profit per unit could be increased to $18, how much B would be produced? Explain how you obtained your answer.

2. What if it was determined that the profit on item C was not actually $14 but was only $12.50. What impact would this have on the total quantities of items A, B and C being produced? What impact would it have on total profit?

3. What is the range of feasibility for the Material 3 RHS?

4. By how much would profit increase if an additional 100 pounds of material 3 could be obtained at its usual cost?

5. What would the total profit equal if an additional 500 pounds of material 3 could be obtained at its usual cost?

6. Do you see any difficulty in allowing a different department (X-Y-Z) to take 100 pounds of material 2? How would this affect A-B-C’s profit?

Subject | Business |

Due By (Pacific Time) | 08/12/2013 11:51 pm |

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