Linear Programming Problem:
A company assembles four products (1, 2, 3, 4) from delivered components. The profit per unit for each product (1, 2, 3, 4) is £12, £15, £22 and £17 respectively. The maximum demand in the next week for each product (1, 2, 3, 4) is 50, 60, 85 and 70 units respectively.
There are three stages (A, B, C) in the manual assembly of each product and the man-hours needed for each stage per unit of product are shown below:
|
|
Product
|
|
1
|
2
|
3
|
4
|
|
Stage
|
A
|
2
|
2
|
3
|
4
|
|
B
|
2
|
2
|
4
|
2
|
|
C
|
1
|
3
|
3
|
1
|
The nominal time available in the next week for assembly at each stage (A, B, C) is 160, 180 and 80 man-hours respectively.
It is possible to vary the man-hours spent on assembly at each stage such that workers previously employed on stage B assembly could spend up to 20% of their time on stage A assembly and workers previously employed on stage C assembly could spend up to 30% of their time on stage A assembly.
Production constraints also require that the ratio (product 1 units assembled)/(product 4 units assembled) must lie between 0.9 and 1.15.
Formulate the problem of deciding how much to produce next week as a linear program and solve it.
Use both MATLAB Optimisation Toolbox and Excel Solver to solve the problem and perform sensitivity analysis. Then formulate another two similar LP problems (with at least 4 design variables) and solve the problems again.
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