Please assist

QUESTION our. Part A A competitive firm has the following production function, q = 60K + 34!. -4KL 6K3 3!? If p is the market price, w is the wage, and r is the rental rate ofcapital, then: (i) Write down the rm's prot function. (3 marks) ' {ii} solve for the optimal K and L. (6 marks) Use the Hessian to check the second order conditions. (3 marks) (iii) Part B A consumer with the following utility function U = icy2 faces two constraints. The rst is the normal budget constraint where he has Gil-15 100 and the price of x and y are both GHe 1. Also. the consumer has been issued [20 ration coupons by the government which he must use whenever he buys either at or 3;. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH3 and 6 coupons. (i) Write down the Lagrangian for this problem. [3 marks) find the optimal x and 3:. Identify (ii) Applying the steps of Kuhn-Tucker, graph of your which constraints are binding. Draw a carefully labelled solution. (10 marks) [Total Marks = 25]