Question 1 • 2024
5 Marks
The marginal cost of producing x units of a product is given by MC = 3x^2 - 12x + 10 . The fixed cost is ₹ 100 . Find: (i) The total cost function C(x) . (ii) The average cost function AC(x) . (iii) The total cost of producing 5 units.
Answer: (i) \ C(x) = x^3 - 6x^2 + 10x + 100 \quad (ii) \ AC(x) = x^2 - 6x + 10 + \frac{100}{x} \quad (iii) \ C(5) = ₹125
Question 2 • 2022
5 Marks
A company manufactures two types of products, A and B . Each unit of A requires 3 hours of machining and 1 hour of polishing. Each unit of B requires 1 hour of machining and 2 hours of polishing. The factory has at most 30 hours of machining and at most 20 hours of polishing available per week. If profit on A is ₹ 300 and on B is ₹ 400 , formulate and solve the LPP to maximize profit.
Answer: \text{Maximum Profit} = ₹4,800 \text{ (producing 8 units of A and 6 units of B)}