the question is shown below in the picture

2. A firm produces output y using two factors of production (inputs), labour L and capital K. The 1 1 firm's production function is f(L, K) = JE + W? = L5 + K5. The wage rate w = 6 and the rental price of capital r = 2 are taken as parameters (fixed) by the firm. a. Show whether this firm's technology exhibits decreasing, constant, or increasing returns to scale. (4) b. Solve the firm's long run cost minimization problem (minimize costs subject to the output constraint) to derive this firm's demand function for labour L = L(y) and for capital K = KM, and the firm's long run total cost function C = CM. (8) c. Suppose in the short run, capital is fixed at K = 100. Derive the firm's short run total cost function C = C(y). (5) d. Derive this firm's short run supply function y = y(p) assuming it is a competitive firm. Note: p is the price of the output y