Maximizing Profit?
Rahul, a small entrepreneur, wants to manufacture a limited quantity of a product to maximize his profit. He has a fixed cost of ₹1000 and a variable cost of ₹15 per unit. If he sells each unit at ₹30, formulate and solve the linear inequality to find the maximum quantity he should produce to achieve the highest profit.
1 Answer
📌 CONCEPT: To maximize profit, Rahul needs to find the maximum quantity of the product he should produce while considering the fixed and variable costs, and the selling price of each unit.
📐 RULE / FORMULA: The profit P(x) can be calculated using the formula P(x) = (selling price - variable cost) × quantity - fixed cost, where x is the quantity produced.
💡 WORKED EXAMPLE: Given that the fixed cost is ₹1000, the variable cost is ₹15 per unit, and the selling price is ₹30 per unit, we can formulate the linear inequality as 30x - 15x - 1000 ≥ 0. Simplifying this inequality, we get 15x ≥ 1000, which gives us x ≥ 1000/15. Therefore, Rahul should produce at least 66.67 units to achieve the highest profit.
⚠️ COMMON MISTAKE: Students often forget to consider the fixed cost while formulating the linear inequality, which can lead to incorrect solutions.
12 Jun 26
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