Help me solve the following questions.,,,

Suppose a price taker firm faces market prices as follows: price of its output is p = 48, price of labor

input is w = 16 and price of capital input is r = 1. Suppose the production function of the this firm is given by

f(L, K) = 6L1/4K1/4.

(a) Find the labor-capital combination (L, K), that produces 120 units at a minimum cost.

(b) Find the profit maximizing quantity level, q?, together with the labor-capital combination thatproduces it, (L?, K?).

A competitive firm uses two inputs, capital (k) and labour (), to produce one output, (y). The price of capital, Wk, is $1 per unit and the price of labor, WI, is $1 per unit. The firm operates in competitive markets for outputs and inputs, so takes the prices as given. The production function is f (k, [) = k0.25 10.5. The maximum amount of output produced for a given amount of inputs is y = f (k, 1) units.1. Write the equations for the firm' 5 average cost function. [2 marks] 6' 2. Write the equations for the firm' 5 marginal cost function. [2 marks] (4 3. Show the rm\" 5 long-run supply function on a diagram and write a supply function for the firm. [3 marks] 4. Using your supply function, nd the prot maximising quantity if the price of output is P=2. What price would be needed for the firm to supply 8 units of output? [4 marks] m, then 1r(p, w') 3 7r(p,w)