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Profit on the Classic bag is £40 and on the Luxury bag £50. The company are planning their weekly work schedule, they want to maximise their profit. The production mix is subject to certain constraints. They must make at least 40 bags in total per week and they can make no more than 60 of the Luxury bag.
The level of production is restricted by the weekly labour availability according to the following table:
| | Classic Requirement | Luxury Requirement |
Availability |
| Fabric Construction | 20 | 30 | 2400 |
| Frame Construction | 30 | 20 | 3000 |
i)
Formulate the objective function and the constraints.
ii)
Draw an accurate graph showing the constraints, the feasible region, and the
vertices of the feasible region.
iii)
Find the optimal solution for the problem using the graphical method and by
calculating profit at each vertex.
iv)
Identify slack/tight variables.
v)
Calculate the shadow price for both fabric and frame construction.
vi)
If the company could increase the time available for fabric construction, by
how much should it be increased? What would be the best product mix and the
resulting profit?
vii)
Looking at the original problem, what would be the optimal solution if the profit on the Luxury bag was increased to £60, the profit on the Classic bag was to remain at £40.
viii)
Following on from vii), if the constraint on the number of Luxury bags was increased to a maximum of 80 per week, what is the best solution?
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