ACCA PM · Guided practice (Show me how)
Chapter 6: Limiting factors
Linear programming: optimum, slack and shadow prices
Peter makes two types of chair - the 'Executive' and the 'Standard'. The data relating to each is as follows:
| Standard | Executive | |
|---|---|---|
| Materials | 2 kg | 4 kg |
| Labour | 5 hours | 6 hours |
| Contribution | $6 | $9 |
There is a maximum of 80 kg of material available each week and 180 labour hours per week. Demand for 'Standard' chairs is unlimited, but maximum weekly demand for 'Executive' chairs is 10.
(a) Find the optimal production plan and the maximum contribution that this will generate. (b) Calculate the slack for each of the constraints. (c) Calculate the shadow price of each of the constraints.
(a) Formulate, graph and solve
Prepare Peter's linear programming model and calculate the optimum quantities of Standard and Executive chairs and maximum contribution.
(b) Slack
Calculate Peter's unused material, labour and demand capacity at the optimum.
(c) Shadow prices
Calculate Peter's shadow prices for material, labour and demand capacity.
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