Question 5 (c)
Product mix under a raw-material quota: ranking by contribution per rupee of material
12 marks
- Time to write
- About 24 minutes
Question
Question 5 (c) · 12 marksNeel Ltd., which makes three products, gave the following data for 2023:
| Toys | Action games | Activity kits | |
|---|---|---|---|
| Selling price per unit | 120 | 80 | 50 |
| Profit/Volume Ratio | 15% | 20% | 40% |
| Sales Potential (units) | 36,000 | 25,000 | 12,000 |
| Raw Material content, as a percentage of variable cost | 50% | 50% | 50% |
Fixed expenses are estimated to be Rs. 68, 00,000. All three products use a single raw material. Raw material is short in supply, and to meet sales demand the company has a quota for the supply of raw materials, for the year, of the value of Rs. 20,00,000 for manufacturing its products.
You are required to:
Keeping in mind the short supply of raw material, find a product mix that will give you maximum profit.
Find the maximum profit.
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
- estimatedFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The fixed expenses are printed as "Rs. 68, 00,000" (with a space); they are read as printed, ₹68,00,000. A well-known version of this problem has ₹6,80,000; the answer shows the figures on that reading too.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Contribution and raw material per unit 3 marks 5 min
- 2 Ranking by contribution per rupee of material 2 marks 3 min
- 3 Product mix within the quota 4 marks 7 min
- 4 Maximum profit and the other reading 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.
Raw material is the key factor, so products are ranked by contribution per rupee of raw material.
Working: contribution and raw material per unit
| Particulars | Toys | Action games | Activity kits |
|---|---|---|---|
| Selling price per unit (₹) | 120 | 80 | 50 |
| P/V ratio | 15% | 20% | 40% |
| Contribution per unit (₹) | 18 | 16 | 20 |
| Variable cost per unit (₹) | 102 | 64 | 30 |
| Raw material per unit, 50% of variable cost (₹) | 51 | 32 | 15 |
| Contribution per ₹1 of raw material (₹) | 0.35 | 0.50 | 1.33 |
Activity kits first (₹1.33 per rupee of material), action games second (₹0.50), toys third (₹0.35).
(i) Product mix for maximum profit
| Rank | Product | Units | Raw material used (₹) | Contribution (₹) |
|---|---|---|---|---|
| 1 | Activity kits (full potential) | 12,000 | 1,80,000 | 2,40,000 |
| 2 | Action games (full potential) | 25,000 | 8,00,000 | 4,00,000 |
| 3 | Toys (balance of material: ₹10,20,000 ÷ ₹51) | 20,000 | 10,20,000 | 3,60,000 |
| Total | 20,00,000 | 10,00,000 |
The best mix is 12,000 activity kits, 25,000 action games and 20,000 toys (of a potential 36,000 toys), which uses the whole raw-material quota of ₹20,00,000.
| Particulars | ₹ |
|---|---|
| Total contribution | 10,00,000 |
| Less: Fixed expenses | 68,00,000 |
| Result: loss | (58,00,000) |
On the fixed expenses as printed (₹68,00,000) no mix can earn a profit; this mix gives the highest contribution and so the smallest loss, ₹58,00,000.
On the other reading of the fixed expenses
If the printed "68, 00,000" is a misprint for ₹6,80,000 (paper note), the same mix is still the best, and the maximum profit is ₹10,00,000 − ₹6,80,000 = ₹3,20,000.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Contribution and raw material per unit | 3 |
| 2 | Ranking by contribution per rupee of material | 2 |
| 3 | Product mix within the quota | 4 |
| 4 | Maximum profit (and the other reading) | 3 |
| Total | 12 |
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