Question 5 (a)
Most profitable product mix at four levels of machine hours, and the best level
18 marks
- Time to write
- About 36 minutes
Question
Question 5 (a) · 18 marksFor its three products A, B and C, the relevant data of Y Ltd. are:
| Particulars | A | B | C |
|---|---|---|---|
| Direct Materials (Rs/units) | 270 | 310 | 240 |
| Direct Labour (Rs/units) | 130 | 260 | 270 |
| Variable Overheads (Rs/units) | 110 | 230 | 180 |
| Selling Price (Rs/unit) | 870 | 1040 | 930 |
| Machine hours Required (per unit) | 12 | 6 | 3 |
At four levels of activity (3,600; 6,000; 8,400 or 10,800 machine hours), the fixed overheads are estimated at Rs. 1,00,000; Rs. 1,50,000; Rs. 2,25,000 and Rs. 3,00,000 respectively. In a cost period, the maximum demand of A, B and C is 500; 310 and 1,800 units respectively. You are required to find out:
at each level, the most profitable product-mix and
the level of activity at which profit would be maximum.
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).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Contribution per machine hour and ranking 5 marks 9 min
- 2 Product mix and profit at each of the four levels 10 marks 18 min
- 3 Level of maximum profit 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? Step 2 carries 10 of the 18 marks: guard its minutes.
Try it first. About 36 minutes for 18 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 machine hour and ranking
| Particulars | A | B | C |
|---|---|---|---|
| Selling price per unit (₹) | 870 | 1,040 | 930 |
| Variable cost per unit (₹): materials + labour + variable overheads | 270 + 130 + 110 = 510 | 310 + 260 + 230 = 800 | 240 + 270 + 180 = 690 |
| Contribution per unit (₹) | 360 | 240 | 240 |
| Machine hours per unit | 12 | 6 | 3 |
| Contribution per machine hour (₹) | 30 | 40 | 80 |
| Rank | III | II | I |
| Maximum demand (units) | 500 | 310 | 1,800 |
| Machine hours for maximum demand | 6,000 | 1,860 | 5,400 |
Machine hours are the limiting factor, so products are taken in the order C, B, A up to their demand.
(i) Most profitable product mix at each level
| Machine hours available | 3,600 | 6,000 | 8,400 | 10,800 |
|---|---|---|---|---|
| C: units (hours) | 1,200 (3,600) | 1,800 (5,400) | 1,800 (5,400) | 1,800 (5,400) |
| B: units (hours) | nil | 100 (600) | 310 (1,860) | 310 (1,860) |
| A: units (hours) | nil | nil | 95 (1,140) | 295 (3,540) |
| Contribution from C (₹) | 2,88,000 | 4,32,000 | 4,32,000 | 4,32,000 |
| Contribution from B (₹) | nil | 24,000 | 74,400 | 74,400 |
| Contribution from A (₹) | nil | nil | 34,200 | 1,06,200 |
| Total contribution (₹) | 2,88,000 | 4,56,000 | 5,40,600 | 6,12,600 |
| Less: Fixed overheads (₹) | 1,00,000 | 1,50,000 | 2,25,000 | 3,00,000 |
| Profit (₹) | 1,88,000 | 3,06,000 | 3,15,600 | 3,12,600 |
At 10,800 hours, 3,540 hours remain for A after C and B, giving 295 units (within A's demand of 500).
Profit is highest, at ₹3,15,600, at the level of 8,400 machine hours, with a mix of C 1,800 units, B 310 units and A 95 units. Moving to 10,800 hours adds ₹72,000 of contribution from A but ₹75,000 of fixed overheads, so profit falls.
Where the 18 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Contribution per machine hour and ranking | 5 |
| 2 | Product mix and profit at each of the four levels | 10 |
| 3 | Level of maximum profit | 3 |
| Total | 18 |
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