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. (a) The inverse demand function and total cost function of a designer handbag manufacturer are given as follows: P = 2000 - 10Q TC = 5000 + 500Q i. Find the manufacturer's total revenue function and profit function in terms of quantity. [2 marks] ii. Using optimisation, find the level of output and price at which the total revenue is maximised, and calculate the maximum revenue that the manufacturer can achieve. Demonstrate that it is a maximum using second-order conditions. [6 marks] intic dad : sec [2 marks] (b) Suppose a firm's production function is given as follows: Q = 10KSL5 where Q is weekly output and K and L are weekly inputs of machine-hours and labour-hours respectively. i. Find the level of output when K=243 hours and L=32 hours. [1 mark] ii. Using the differential method, find the approximate percentage change in Q, when L and K increase by 2%. Comment on your result. [4 marks