Problems:
The Eastside Manufacturing Company produces four different aircraft components from fabricated sheet metal for several major aircraft companies. The manufacturing process consists of four operations - stamping, assembly, finishing, and packaging. The processing time per unit for each of the operations and total available hours per year to produce these components are given below.
|
Operation
|
Component (hr/unit)
|
Total Hours per Year
|
|
1
|
2
|
3
|
4
|
|
Stamping
|
0.06
|
0.17
|
0.10
|
0.14
|
700
|
|
Assembly
|
0.18
|
0.20
|
--
|
0.14
|
700
|
|
Finishing
|
0.07
|
0.20
|
0.08
|
0.12
|
800
|
|
Packaging
|
0.09
|
0.12
|
0.07
|
0.15
|
600
|
The sheet metal required for each component, the estimated annual demand, and the profit contribution provided by each component, are as follows:
|
Component
|
Sheet Metal
(ft2)
|
Estimated Annual Demand
|
Profit Contribution
$
|
|
1
|
2.6
|
2,600
|
90
|
|
2
|
1.4
|
1,800
|
100
|
|
3
|
2.5
|
4,100
|
80
|
|
4
|
3.2
|
1,200
|
120
|
The company has 15,000 square feet of fabricated metal delivered each month. The company has the following prioritized production goals for these components:
- Avoid the use of overtime given the low profit margins.
- Meet all component demand.
- Achieve an annual profit contribution of at least $700,000
- Avoid additional material orders - pricing is dependent upon annual contracts with fixed amounts and delivery schedules
a. Formulate a linear programming model to determine the quantity of each component to produce to achieve the company's goals.
b. Determine the solution that will best achieve the company's goals in component production, including the quantity of each component produced, the annual profit contribution attained, and the levels of goal achievement.
c. Determine how the solution would be affected if the first two goal priorities were reversed