Being the good <?xml:namespace prefix = st1 ns = \"urn:schemas-microsoft-com:off

Question

Being the good <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" />COO that you are, you are always looking for ways to minimize costs and increase profitability.  You suspect that there is much room for improvement in this regard. Specifically, you have reason to believe that production and stocking levels of each plant and warehouse could be modified to yield the desired results.

The details of this managerial challenge are as follows:

Production Costs   -    Plant A -- $100 per circuit board

            Plant B -- $120 per circuit board

            Plant C -- $90 per circuit board

            Plant Capacity       -    Plant A

Explanation / Answer

Let A1 be the number of boards sent from plant A to warehouse1.

Similarly we can have A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, C4. These are our 12 variables.

profit(A1) = 150-100-10 = $40 (this is nothing but selling-(cost+shipping))

we can calculate the other 12 in a similar fashion.

profit(A2) = $35

profit(A3) = $10

profit(A4) = $20

profit(B1) = -$20

profit(B2) = $10

profit(B3) = $5

profit(B4) = $10

profit(C1) = $35

profit(C2) = $15

profit(C3) = $30

profit(C4) = $38

We have constraints here.

1. A1+A2+A3+A4 <= 1200 (That the capacity of the plantA)

2. B1+B2+B3+B4 <= 1200 (That the capacity of the plantB)

3. C1+C2+C3+C4 <= 500 (That the capacity of the plantC)

Also, we need to meet the demand.

4. A1 + B1 + C1 = 700 (Thats the demand from warehouse1)

5. A2 + B2 + C2 = 700 (Thats the demand from warehouse2)

6. A3 + B3 + C3 = 700 (Thats the demand from warehouse3)

7. A4 + B4 + C4 = 700 (Thats the demand from warehouse4)

These are the 7 constraints of our linear program with 3 inequalities and 4 equalities.

Our objective is to maximize the profit. Hence our objective function will be the following.

Maximize(40*A1 + 35*A2 + 10*A3 + 20*A4 - 20*B1 + 10*B2 + 5*B3 + 10*B4 + 35*C1 + 15*C2 + 30*C3 + 38*C4).

(Here 40*A1 is the profit from the boards sent from plantA to warehouse1 , and others are similar)

This is the final linear program. with the objective function and the 7 constraints.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.