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Homework answers / question archive / Santana Rey has found that Business Solutions’s line of computer desks and chairs has become very popular, and she is finding it hard to keep up with demand
Santana Rey has found that Business Solutions’s line of computer desks and chairs has become very popular, and she is finding it hard to keep up with demand. She knows that she cannot fill all of her orders for both items, so she decides she must determine the optimal sales mix given the resources she has available. Information about the desks and chairs follows.
| Desks | Chairs | |||||
| Selling price per unit | $ | 1,125 | $ | 375 | ||
| Variable costs per unit | 500 | 200 | ||||
| Contribution margin per unit | $ | 625 | $ | 175 | ||
| Direct labor hours per unit | 5 | hours | 4 | hours | ||
| Expected demand for next quarter | 175 | desks | 50 | chairs | ||
Santana has determined that she only has 1,015 direct labor hours available for the next quarter and wants to optimize her contribution margin given the limited number of direct labor hours available.
Required:
Determine the optimal sales mix and the contribution margin the business will earn at that sales mix. (Round per unit amounts to 2 decimal places.)
| desk | chairs | ||
| contribution per DL | |||
| desk | chairs | total | |
| maximum units to be sold | 175 | 50 | |
| hours required to produce maximum | |||
| For most profitable sales mix: | |||
| desk | chairs | total | |
| hours dedicated to the product | 1015 | ||
| units produced | |||
| contribution margin per unit | |||
| total contribution margin |
| Solution | |||||||
| Step-1 | |||||||
| Desks | Chairs | ||||||
| Selling price per unit | 1,125 | 375 | |||||
| Variable costs per unit | 500 | 200 | |||||
| Contribution margin per unit | 625 | 175 | |||||
| Direct labor hours per unit | 5 | hours | 4 | hours | |||
| Contribution Per Labour hour | 125 | 43.75 | |||||
| Rank Based on Contribution per Labour Hour | 1 | 2 | |||||
| From the above calculation it is clear that desks have more contribution per limiting factor here labour hour | |||||||
| So desks ranked 1 and Chairs ranked 2. | |||||||
| So in order to maximise profit we have to produce desks to the maximum demand and Chairs for the balance labour hours. | |||||||
| Step-2 | |||||||
| Total Labour hours Available | 1015 | hours | |||||
| Number of Desks to be produced | 175 | desks | |||||
| Direct labor hours per unit | 5 | hours | |||||
| Total Labour hours for Desks | 875 | hours | |||||
| Balance hours Available | 140 | hours | (1015-875) | ||||
| Direct labor hours per unit | 4 | hours | |||||
| Number of Desks to be produced | 35 | Chairs | (140/4) | ||||
| Step-3 | |||||||
| Desks | Chairs | ||||||
| hours dedicated to the product | 875 | 140 | 1015 | ||||
| units produced | 175 | 35 | |||||
| contribution margin per unit | 625 | 175 | |||||
| total contribution margin |
