Optimization Model for a Company?

📌 CONCEPT: We need to formulate an optimization model to determine the optimal production level that maximizes the profit of the company, given the revenue and production costs.

📐 RULE / FORMULA: The profit function P(x) is given by P(x) = Total Revenue - Total Cost, where Total Revenue = Selling Price * Number of Units, and Total Cost = Variable Cost * Number of Units + Fixed Cost.

💡 WORKED EXAMPLE: Let's assume the company produces x units of the product. The selling price is ₹200 per unit, the variable cost is ₹100 per unit, and the fixed cost is ₹50,000. The profit function is P(x) = 200x - (100x + 50000) = 100x - 50000. To maximize profit, we need to find the critical point of the function by taking its derivative and setting it equal to zero. This gives dP/dx = 100.