A company makes 4 products P1, P2, P3 and P4. The raw materials (A, B, C)...
A company makes 4 products P1, P2, P3 and P4. The raw materials (A, B, C) and the labor hours needed to produce each product is given the table. Also the profit per each of these products is given.
|
A |
B |
C |
Labor hours |
Profit per each |
|
|
P1 |
4 |
0 |
1 |
3 |
$24 |
|
P2 |
0 |
4 |
0 |
1 |
$28 |
|
P3 |
2 |
2 |
2 |
2 |
$20 |
|
P4 |
3 |
1 |
1 |
1 |
$25 |
During next week, the company has:
2800 units of A,
3000 units of B,
1000 units of C
1800 hours of labor available.
The firm operates to achieve maximum profit.
a) Define the variables and formulate the LP.
b) Solve it on Excel and report maximum profit and how much of each products should be produced?
c) Is there any C left over? If so, how much? If not, what is its shadow price (dual value)? Explain what this value means to management.
d) Is there any B left over? If so, how much? If not, what is its shadow price (dual value)? Explain what this value means to management.
e) Interpret the meaning of the lower bound to Labor. That is, explain how the solution would change if the amount of labor fell below that lower value.
f) What is the meaning of reduced cost for each product?
g) Interpret the meaning of the allowable increase and decreases for the objective coefficients.
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