Suppose that the firm uses three inputs to produce its output: capital K, labor, L and materials, M. The firm’s production function is given by Q = K^ (1/3) * L ^ (1/3) * M ^ (1/3). The prices of capital, labor, and materials are r=1, w=1, and m=1 respectively. A) What is the solution to the firm’s long-run cost-minimization problem given that the firm wants to produce Q of output? B) B What is the solution to the firm’s short-run cost-minimization problem when the firm wants to produce Q units and capital is fixed at K ( K is denoted with a bar above it which I can not do on this) . C) When Q= 4, the long-run cost-minimization quantity of capital is 4. IF capital is fixed at (K-bar) = 4 in the short-run, show that the short-run and long-run cost-minimizing quantities of labor and materials are the same.