A manufacturing company sells high-quality wireless headphones through a chain of specialty shops. The demand equation for these headphones is: P = 500 - 10Q where P is the selling price (in $ per unit) and Q is the quantity demanded (in thousands of headphones). The company's total cost function is given by C = 400*In(Q+5) + 100 a. (2 marks) At Q = 4, the revenue is (thousand dollars) and the profit is (thousand dollars) (Round your answer to 2 decimal places) b. (2 marks) For which value or & is there unit elasticity of demand for the headphones? (Round your answer to 2 decimal places) thousand headphones c. (1 mark) How many headphones must be sold to maximise profit? (Round your answer to 2 decimal places) thousand headphones d. (1 mark) What is the value of the second derivative of the profit function at the maximum found in the previous question? (Round your answer to 2 decimal places)