Kindly help me solve this problem

A firm uses inputs of labor, L, and capital, K, to produce its output, Q, according to the production function Q=f(X,L)-9LUSKVS. The firm is a price-taker in the input markets. Labor is paid an hourly wage of w = 12, and the price of capital is r =6. The firm sells its output at a price of p = 4 per unit. 1) Maximize the profit function to determine the optimum level of each input the firm should use. 2) Check second-order sufficient condition. Show your calculations.Problem 2 Consider an exchange economy with two goods and two consumers. Consumer 1 has en- dowment wl = (2,2) and utility function u ($11, 121) = (In, + 21")'. 1/2\\2 Consumer 2 has endowment w? = (3, 1) and utility function u2($12, 122) - $12 22 . 1/4 3/4 (a) Compute the Marshallian demands for each consumer at arbitrary income levels m, (for consumer 1) and my (for consumer 2). (b) Replace m, with the market value of w' to get demands r' (p, w ) (consumer 1) and I' (p, w?) (consumer 2). (c) Find a competitive equilibrium for this economy.Let X be a random variable which has mean & # 0 and variance o?. Let Y be another random variable which has the same mean / and variance o', and suppose the correlation between X and Y is p, where -1