4) Assume has two inputs in production, labor (L) and capital (K). The production function is given as: 1 q(L K) =2 LV . K2 Also, assume that, in the short-run, the firm has already invested in 8 units of capital (K =9). a. Solve for the function L(q) which defines the quantity of labor required to produce any given level of output in the short-run (hint: plug K into production function and solve for L). b. Suppose the firm must pay a wage of w = 3 dollars for each unit of labor. Solve for the function MC(q) that defines the firm's marginal cost of production for any level of output. (hint: plug L(qg) from part a into the cost functions). c. Ifthe firm can sell each unit of output at a price of p = 45 dollars, what is their profit maximizing level of output