Question

To manufacture ‘x’ number of dolls, a company’s total cost function C(x) is given by C (x) = 100 + 0.025x² and the total revenue function R(x) is described as R(x) = 5x. Given that C(x) and R(x) are in thousand rupees, what number of dolls shall be manufactured to maximise the profit of the company? What is the maximum profit?

Answer 1

P(x) = R(x) – C(x) = 5x – (100 + 0.025x²) 

⇒ P’(x) = 5 – 0.05 x ⇒ x = 100 

As P’’(x) = −0.05 < 0, ∀ x 

∴ Manufacturing 100 dolls will maximise the profit of the company 

And, Profit = ₹ 1,50,000