Question 5 OR (b)
Optimum product mix with machine Z as the bottleneck
12 marks
- Time to write
- About 24 minutes
Question
Question 5 OR (b) · 12 marksMeera Ltd., makes three products A, B and C, each of which uses three different machines X, Y and Z. The relevant data for June, 2024 are:
| Product | A | B | C |
|---|---|---|---|
| Selling Price per unit (Rs) | 11,000 | 8,400 | 6,200 |
| Variable cost per unit (Rs.) | 7,600 | 5,800 | 4,200 |
| Machine-wise hours required per unit: | |||
| Machine X | 20 | 12 | 5 |
| Machine Y | 20 | 16 | 6 |
| Machine Z | 20 | 6 | 2 |
| Expected Demand (units) | 220 | 220 | 220 |
Machine Z has been identified as the bottleneck, with capacity limited to 5,600 hours. From the above information calculate the optimum product mix, and ascertain the total profit at that mix if fixed cost amounts to Rs.8,00,000
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Contribution per Z hour and ranking 4 marks 7 min
- 2 Allocation of machine Z hours and optimum mix 5 marks 8 min
- 3 Total profit 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 24 minutes for 12 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Contribution per bottleneck hour and ranking
With machine Z as the bottleneck, products are ranked by contribution per machine-Z hour.
| Particulars | A | B | C |
|---|---|---|---|
| Selling price per unit (₹) | 11,000 | 8,400 | 6,200 |
| Less: Variable cost per unit (₹) | 7,600 | 5,800 | 4,200 |
| Contribution per unit (₹) | 3,400 | 2,600 | 2,000 |
| Machine Z hours per unit | 20 | 6 | 2 |
| Contribution per Z hour (₹) | 170 | 433.33 | 1,000 |
| Rank | III | II | I |
Although A earns the most per unit, it earns the least per hour of the scarce machine Z.
| Product (in order of rank) | Units | Machine Z hours used | Contribution (₹) |
|---|---|---|---|
| C (full demand: 220 × 2 hours) | 220 | 440 | 4,40,000 |
| B (full demand: 220 × 6 hours) | 220 | 1,320 | 5,72,000 |
| A (balance: 3,840 hours ÷ 20 hours) | 192 | 3,840 | 6,52,800 |
| Total | 5,600 | 16,64,800 |
Hours left for A = 5,600 − 440 − 1,320 = 3,840, enough for 192 of the 220 units demanded. The optimum mix is A 192 units, B 220 units and C 220 units.
| Particulars | ₹ |
|---|---|
| Total contribution | 16,64,800 |
| Less: Fixed cost | 8,00,000 |
| Profit | 8,64,800 |
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Contribution per Z hour and ranking | 4 |
| 2 | Allocation of machine Z hours and optimum mix | 5 |
| 3 | Total profit | 3 |
| Total | 12 |
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