Cheapest Stock Mix for a ₹1 Lakh Profit Target
A neighbourhood electronics store sells two models of an inverter. The Basic model costs the store ₹8,000 and is sold at a 20% margin on cost; the Pro model costs ₹20,000 and is sold at a 15% margin on cost. Last month the store could sell at most 60 Basic units (supplier limit) and at most 25 Pro units (showroom space), and the two together could not exceed 70 units because of storage.
The owner has set a monthly profit target of ₹1,00,000 and wants to block the least possible capital in stock while meeting it. His accountant has already prepared a plan of 60 Basic and 25 Pro, arguing that stocking the maximum of both models is the safest way to clear the target. The owner is not convinced: he points out that the plan blocks ₹9,80,000 and asks whether a smaller outlay can still deliver ₹1,00,000.
Assume whole units only, that stock is bought to order, and that whatever is stocked is sold.
1. Find the stock mix that meets the ₹1,00,000 profit target with the least capital blocked.
Read the worked answer
Profit per unit: Basic = 20% of ₹8,000 = ₹1,600; Pro = 15% of ₹20,000 = ₹3,000. Capital per unit: ₹8,000 and ₹20,000.
Fix the number of Pro units and take the smallest feasible number of Basic units:
| Pro (P) | Basic needed (1,600B ≥ 1,00,000 − 3,000P) | Capital |
|---|---|---|
| 0 | 63 needed - capped at 60 | target missed (max ₹96,000) |
| 1 | B ≥ 60.6 → 61 | not allowed (cap 60) |
| 2 | B ≥ 58.75 → 59 | 4,72,000 + 40,000 = ₹5,12,000 |
| 3 | B ≥ 56.875 → 57 | 4,56,000 + 60,000 = ₹5,16,000 |
| 4 | B ≥ 55 → 55 | 4,40,000 + 80,000 = ₹5,20,000 |
Capital rises with each extra Pro because Pro ties up more money per rupee of profit. The minimum is 59 Basic + 2 Pro: capital ₹5,12,000, profit ₹1,00,400, units 61 (within the 70 cap). Note that this uses one Basic unit fewer than the intuitive 60 + 2 plan and saves ₹8,000 while still clearing the target.
2. The accountant also suggests stocking nothing but Pro. Evaluate that suggestion and state the profit-maximising mix.
Read the worked answer
Only-Pro fails on two counts. The cap is 25 Pro units, giving profit 25 × 3,000 = ₹75,000 - short of ₹1,00,000 by ₹25,000. And the display cap of 70 units would be idle while capital of ₹5,00,000 earns less per rupee than Basic does (15% versus 20% on cost).
Profit-maximising mix: fill the higher absolute profit per unit first, subject to all caps - 25 Pro and 45 Basic = 70 units. Profit = 75,000 + 72,000 = ₹1,47,000; capital = 5,00,000 + 3,60,000 = ₹8,60,000.
That mix is not the answer to the first task because the objectives differ. Minimising capital for a fixed profit is driven by profit per rupee of capital (Basic is better); maximising profit for a fixed capital or space is driven by profit per unit of the binding constraint (Pro is better here). The accountant's "maximum of both" plan is neither: it blocks ₹9,80,000 to earn ₹1,71,000, which is more capital than either objective requires.
3. If the supplier cuts the Basic-model limit to 55 units, what is the least capital needed to still hit ₹1,00,000?
Read the worked answer
With Basic capped at 55, the maximum Basic profit is 55 × 1,600 = ₹88,000, leaving ₹12,000 to be found from Pro at ₹3,000 each - so 4 Pro units are required.
Check everything: profit = 88,000 + 12,000 = ₹1,00,000 exactly; units = 59, within the 70-unit storage cap; Pro at 4 is well within its own cap of 25.
Capital = 55 × 8,000 + 4 × 20,000 = 4,40,000 + 80,000 = ₹5,20,000.
This is the unique minimum: 3 Pro units would give only ₹97,000, and any substitution of Pro for Basic increases capital per rupee of profit, so no other mix at or above the target is cheaper. The pattern is consistent with the earlier result - as the cheap-profit item is squeezed, the outlay needed to reach the same target rises.