Worked Solution
✓ VerifiedProduct Mix and Profit Maximization — MNP Company Limited
Step 1: Identify the Limiting Factor
The scarce resource is machine hours (55,000 hours available). To allocate machine hours optimally, we must calculate Contribution per Machine Hour for each product.
Step 2: Machine Hours per Unit
Variable factory overheads are charged at ₹4 per machine hour.
- Product A: ₹40 ÷ ₹4 = 10 machine hours per unit
- Product B: ₹20 ÷ ₹4 = 5 machine hours per unit
Step 3: Contribution per Unit
Contribution = Selling Price − Variable Cost (DM + DL + Variable OH)
- Product A: ₹180 − (₹55 + ₹35 + ₹40) = ₹180 − ₹130 = ₹50 per unit
- Product B: ₹175 − (₹60 + ₹45 + ₹20) = ₹175 − ₹125 = ₹50 per unit
Step 4: Contribution per Machine Hour (Key Ratio)
- Product A: ₹50 ÷ 10 hours = ₹5 per machine hour
- Product B: ₹50 ÷ 5 hours = ₹10 per machine hour
Ranking: Product B (Rank 1) → Product A (Rank 2)
Step 5: Optimal Product Mix
Allocate machine hours first to Product B (higher-ranked), then to Product A with remaining hours.
- Product B: 6,000 units × 5 hours = 30,000 hours used
- Remaining hours: 55,000 − 30,000 = 25,000 hours
- Product A: 25,000 ÷ 10 = 2,500 units
Optimal Mix: Product A — 2,500 units; Product B — 6,000 units
Step 6: Profit Calculation
Total Contribution = (2,500 × ₹50) + (6,000 × ₹50) = ₹1,25,000 + ₹3,00,000 = ₹4,25,000
Less: Fixed Expenses = ₹1,60,000
Maximum Profit = ₹2,65,000 per month
Write it like this
1The skeleton
- Start with the limiting factor identification line — write 'The scarce resource is machine hours (55,000 hours available)' as your very first sentence; examiners award 1 mark just for correctly naming the constraint upfront.
- Derive machine hours per unit from the overhead rate — don't assume hours, divide variable OH per unit by ₹4/hour; showing this working (40÷4=10, 20÷4=5) is where most of your Step 2 marks sit.
- Build a ranking table with Contribution/Machine Hour — lay out SP, VC, Contribution, Hours/unit, and Contribution per hour in a clean columnar format; examiners follow tables faster than prose and tick each row.
- State the ranking explicitly before allocation — write 'Product B is ranked 1, Product A is ranked 2' as a standalone line; it shows your decision logic and connects Step 4 to Step 5 without ambiguity.
- Show hour allocation step-by-step with balancing figure — write 6,000×5=30,000 → balance 25,000 → 25,000÷10=2,500 units of A; the balancing figure line is what separates a 4/5 from a 5/5.
- End with a Profit Statement box — Total Contribution minus Fixed Expenses equals Profit; label it 'Maximum Profit = ₹2,65,000 per month' so the examiner doesn't have to hunt for your final answer.
2Examiner-rewarded phrases
3Common trap
Watch out — students calculate equal contribution per unit (₹50 = ₹50) and conclude both products are equally profitable, then produce the wrong mix or skip ranking entirely. The whole question hinges on contribution per machine hour, not per unit — missing that step means your allocation is wrong and you drop 3-4 marks even if your arithmetic is perfect.