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Imagine Rajesh & Co. Pvt. Ltd. makes two products — a premium chair and a basic stool. Both are profitable. But raw material is scarce. Which one should they push harder? That's the Sales Mix Decision — choosing the best combination of products to maximise profit when a limiting factor (also called a key factor or bottleneck resource) exists.

Here's the core rule: when a limiting factor exists, rank products by Contribution per unit of the limiting factor — NOT by contribution per unit alone. The limiting factor is whatever resource is in short supply — machine hours, labour hours, raw material kg, etc. You divide each product's contribution per unit (Selling Price minus Variable Cost) by the units of the limiting factor it consumes. The product with the highest ratio gets produced first. Fill demand for that product, then move to the next, until the resource runs out.

When there is no limiting factor, every unit of every product that earns a positive contribution should be produced — just sell as much as demand allows. The mix problem only gets interesting (and exam-worthy) when supply is constrained. Also watch out: if the question gives a fixed sales mix (say, always 2 units of A for every 3 of B), then calculate a weighted average P/V ratio using that mix and apply it to find the overall Break-Even Point. The formula is: BEP (₹) = Fixed Costs ÷ Weighted Average P/V Ratio. This multi-product BEP variant is asked frequently as a 5-mark question in Paper 4. One more nuance — always check maximum demand constraints. Even if Product A ranks #1, you can only produce up to its maximum demand before shifting remaining resources to Product B.

📊 Worked example

Example 1 — Optimal Product Mix with Limiting Factor

Sharmaji's factory produces two products, X and Y. Machine hours available: 1,800 hours/month.

| | Product X | Product Y |

|---|---|---|

| Selling Price | ₹1,200 | ₹1,000 |

| Variable Cost | ₹700 | ₹500 |

| Contribution/unit | ₹500 | ₹500 |

| Machine hrs/unit | 3 hrs | 2 hrs |

| Max Demand | 400 units | 500 units |

Step 1 — Contribution per machine hour (limiting factor):

  • Product X: ₹500 ÷ 3 = ₹166.67/hr
  • Product Y: ₹500 ÷ 2 = ₹250.00/hr ← Higher, so Rank 1

Step 2 — Allocate machine hours:

  • Product Y (Rank 1): 500 units × 2 hrs = 1,000 hrs used → Balance = 800 hrs
  • Product X (Rank 2): 800 hrs ÷ 3 = 266 units (max demand 400, but limited by hours)

Step 3 — Total Contribution:

  • Product Y: 500 × ₹500 = ₹2,50,000
  • Product X: 266 × ₹500 = ₹1,33,000
  • Total Contribution = ₹3,83,000

---

Example 2 — Weighted Average P/V Ratio & Multi-Product BEP

Ms. Iyer's firm sells Products A and B always in ratio 3:2. Fixed costs = ₹1,80,000.

| | A | B |

|---|---|---|

| Selling Price | ₹400 | ₹300 |

| Variable Cost | ₹280 | ₹180 |

| Contribution | ₹120 | ₹120 |

| P/V Ratio | 30% | 40% |

| Mix ratio | 3 | 2 |

Weighted Avg P/V Ratio = (30% × 3 + 40% × 2) ÷ 5 = (90 + 80) ÷ 5 = 34%

BEP (₹) = ₹1,80,000 ÷ 0.34 = ₹5,29,412 (approx.)

BEP sales split: A = ₹5,29,412 × 3/5 = ₹3,17,647 | B = ₹2,11,765

⚠️ Common exam mistakes

  • Ranking by contribution/unit instead of contribution/limiting factor unit. In Example 1 above, both products had ₹500 contribution — students often call it a tie. Wrong. Always divide by the hours/kg consumed. The ranking can flip entirely.
  • Ignoring maximum demand constraints. Don't produce 600 units of the top-ranked product if max demand is only 400. Cap at demand, then allocate remaining resources to the next product.
  • Using revenue (selling price) instead of contribution for the P/V ratio. P/V Ratio = Contribution ÷ Sales, not Profit ÷ Sales. Profit is after fixed costs; contribution is before.
  • Calculating BEP with a simple average P/V ratio in a multi-product scenario. You must use the weighted average based on the sales mix — a simple average assumes equal weights, which is almost never the case.
  • Forgetting to state the optimal mix in units AND check feasibility. Exam answers that give only the ranking without showing final units produced and total contribution lose presentation marks. Always conclude with the production plan and total contribution figure.
📖 Reference: Sales Mix — Institute of Chartered Accountants of India
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