To maximize profit with a limited material supply of 500 kg per month, the company should prioritize
producing the product that generates the highest contribution margin per kg of material used.
Step 1: Calculate Contribution Margin Per Unit for Each Product
Since fixed costs are not relevant in this decision, we focus on the contribution margin per unit of raw
material:
Product X
Selling price per unit = $10
Material cost per unit = 2 kg × $1/kg = $2
Contribution margin per unit = $10 - $2 = $8
Contribution margin per kg = $8 ÷ 2 kg = $4 per kg
Product Y
Selling price per unit = $13
Material cost per unit = 6 kg × $1/kg = $6
Contribution margin per unit = $13 - $6 = $7
Contribution margin per kg = $7 ÷ 6 kg = $1.17 per kg
Step 2: Prioritize Product with Higher Contribution Margin Per Kg
Product X ($4 per kg) is more profitable per kg than Product Y ($1.17 per kg).
To maximize profit, produce as many units of Product X as possible first, then allocate the remaining
material to Product Y.
Step 3: Allocate Limited Material (500 kg)
First, maximize production of Product X
Each unit of Product X requires 2 kg.
Maximum units of Product X = 500 kg ÷ 2 kg per unit = 250 units.
However, demand is only 70 units, so produce 70 units of Product X.
Material used for 70 units of X = 70 × 2 kg = 140 kg.
Material remaining = 500 kg - 140 kg = 360 kg.
Use remaining material for Product Y
Each unit of Product Y requires 6 kg.
Maximum units of Product Y = 360 kg ÷ 6 kg per unit = 60 units.
Final Decision:
Produce 70 units of Product X (to meet demand).
Produce 60 units of Product Y (using the remaining material).
IIA Reference for Validation:
IIA GTAG 13: Business Performance Management – Discusses maximizing profit by prioritizing high
contribution margin products.
IIA Practice Guide: Cost Analysis for Decision-Making – Covers constraints and resource allocation for
maximizing profitability.
Thus, B (60 units) is the correct answer because it optimally allocates the 500 kg of material to
maximize profit.
