A retailer stocks two products, A and B.

Annual demand: $D_A = 12{,}000$ units, $D_B = 8{,}000$ units.

Holding cost per unit per year: $h_A = ₦2$, $h_B = ₦3$.

The ordering cost for a combined order (which may contain both products) is $S = ₦5{,}000$.

Because of limited space, the average total inventory ( $\frac{Q_A}{2} + \frac{Q_B}{2}$ ) cannot exceed 5,000 units.

Assuming the retailer orders the two items together so that the order cycle is the same for both products, determine the order quantities $Q_A$ and $Q_B$ that minimise the total annual cost (ordering plus holding) while satisfying the space constraint. Give the quantities to the nearest whole unit.

Question

A retailer stocks two products, A and B.

Annual demand: $D_A = 12{,}000$ units, $D_B = 8{,}000$ units.

Holding cost per unit per year: $h_A = ₦2$, $h_B = ₦3$.

The ordering cost for a combined order (which may contain both products) is $S = ₦5{,}000$.

Because of limited space, the average total inventory ( $\frac{Q_A}{2} + \frac{Q_B}{2}$ ) cannot exceed 5,000 units.

Assuming the retailer orders the two items together so that the order cycle is the same for both products, determine the order quantities $Q_A$ and $Q_B$ that minimise the total annual cost (ordering plus holding) while satisfying the space constraint. Give the quantities to the nearest whole unit.

Accepted Answer

Q_A ≈ 5,477 units, Q_B ≈ 3,651 units

Gce Model Questions Vol1 2024 Commerce Question 24

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