Question 11.A.13: (a) A business makes three different products, as follows:
(a) A business makes three different products, as follows:
| Product (code name) | B14 | B17 | B22 |
| Selling price per unit | $250 | $200 | $230 |
| Variable cost per unit | $100 | $80 | $120 |
| Weekly demand (units | 25 | 20 | 30 |
| Machine time per unit | 4 hours | 3 hours | 4 hours |
Fixed costs are not affected by the choice of product because all three products use the same machine. Machine time is limited to 148 hours a week. Which combination of products should be manufactured if the business is to produce the highest profit?
(b) What steps could lead to a higher level of contribution?
(c) What maximum price would the business logically be prepared to pay to have the remaining B14s machined by a subcontractor, assuming that no fixed or variable costs would be saved by not machining in-house? Would there be a different maximum if we were considering the B22s?
(a)
| Product | B14 | B17 | B22 |
| Selling price per unit | $250 | $200 | $230 |
| Variable cost per unit | $100 | $80 | $120 |
| Contribution per unit | $150 | $120 | $110 |
| Machine time per unit | 4 hours | 3 hours | 4 hours |
| Contribution per machine hour | $37.50 | $40.00 | $27.50 |
| Order of priority | 2nd | 1st | 3rd |
| Therefore: produce | |||
| 20 units of product B17 using | 60 hours | ||
| 22 units of product B14 using | 88 hours | ||
| using 148 hours in total. | |||
This leaves the market demand unsatisfied for a further three units of product B14 and 30 units of product B22.
(b) Some possibilities for improving matters are as follows:
- Contemplate obtaining additional machine time by obtaining a new machine, subcontracting the machining to another business or, perhaps, squeezing a few more hours per week out of the business’s own machine. Perhaps two or more of these strategies could be combined.
- Redesign the products in a way that requires less time per unit on the machine.
- Increase the price per unit of the three products. This may dampen demand, but the existing demand cannot be met at present and it may be more profitable, in the long run, to make a greater contribution on each unit sold than to take one of the other courses of action to overcome the problem.
(c) If the remaining three B14s were subcontracted at no cost, the business could earn a contribution of $150 per unit, which it could not do otherwise. For any price up to $150 per unit, therefore, it would be worth paying a subcontractor to do the machining. Naturally, the business would prefer to pay as little as possible, but anything up to $150 would still make it worthwhile to subcontract the machining. This would not be true of the B22s because they have a different contribution per unit; $110 would be the relevant figure in their case.