- 20 Marks
MA – L2 – Q45 – Decision making techniques
Compute units of each product for Image Solutions to maximize profit and calculate contribution at optimal mix, considering machine hour constraints.
Question
Image Solutions Limited deals in various products. Relevant details of the products are as under:
| PW | PX | PY | PZ | |
|---|---|---|---|---|
| Estimated annual demand (units) | 5,000 | 10,000 | 7,000 | 8,000 |
| Sales price per unit (GH¢) | 150 | 180 | 140 | 175 |
| Material consumption: | ||||
| R (kg) | 2 | 2.5 | 1.5 | 1.75 |
| T (kg) | 0.5 | 0.6 | 0.4 | 0.65 |
| Labour hours | 2 | 2.25 | 1.75 | 2.5 |
| Variable overheads (based on labour cost) | 75% | 80% | 100% | 90% |
| Fixed overheads per unit (GH¢) (based on 80% capacity utilisation) | 10 | 20 | 14 | 16 |
| Machine hours required: | ||||
| Processing machine hours | 5 | 6 | 8 | 10 |
| Packing machine hours | 2 | 3 | 2 | 4 |
Company has a long term contract for purchase of material R and T at a price of GH¢ 15 and GH¢ 20 per kg respectively. Wage rate for 8 hours shift is GH¢ 200.
The estimated overheads given in the above table are exclusive of depreciation expenses. The company provides depreciation on number of hours used basis. The depreciation on each machine based on full capacity utilisation is as follows:
| Hours | GH¢ | |
|---|---|---|
| Processing machine | 150,000 | 150,000 |
| Packing machine | 100,000 | 50,000 |
The company has launched an advertising campaign to promote the sale of its products. GH¢ 2 million have been spent on such campaign. This cost is allocated to the products on the basis of sale.
Required:
Compute the number of units of each product that the company should produce in order to maximize the profit and also compute the product wise and total contribution at optimal product mix.
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