The Kartick Company is trying to determine how much of each of two products to produce over the coming planning period. There are three departments, A, B and C, with limited labor hours available in each department. Each product must be processed by each depart- ment and the per-unit requirements for each product, labor hours available, and per-unit profit are as shown below.
|
Department
|
Product (hrs./unit)
Product 1 Product 2
|
Labor Hours Available
|
|
A
|
1.00
|
0.30
|
100
|
|
B
|
0.30
|
0.12
|
36
|
|
C
|
0.15
|
0.56
|
50
|
|
Profit Contribution
|
$33.00
|
$24.00
|
|
A linear program for this situation is as follows:
Let x1 = the amount of product 1 to produce
x2 = the amount of product 2 to produce
Maximize 33 x1 + 24 x2
s.t.
1.0 x1 + .30 x2 100 Department A
.30 x1 + .12 x2 36 Department B
.15 x1 + .56 x2 50 Department C
x1, x2 > 0
Mr. Kartick (the owner) used trial and error with a spreadsheet model to arrive at a solution. His proposed solution is x1 = 75 and x2 = 60, as shown below in Figure below. He said he felt his proposed solution is optimal.
Is his solution optimal? Without solving the problem, explain why you believe this solution is optimal or not optimal.
FIGURE MR. KARTICK'S TRIAL-AND-ERROR MODEL
