worker-owned firm produces output, Q, according to the following production function:where K is capital and L is la bor (i.e., number of workers). The firm sells its output at price, p. The cost of c a pita l is r. This firm is owned by its workers who all have an equal stake in the firm's profits. Thus, the workers collectively seek to maximizeprofits per worker.(a) Write down this firm's object ive function.(b)List the first order conditions that describe the optimal choice of capital and labor for this firm.(c) What must the marginal revenue product of labor equal if this f ir m is to ma ximize average profits? P rovide an interpretation of this condition.(d)Set up the Hessian for this problem and give the conditions that must hold in order to guarantee the firm's choice of K and L maximizes profits per worker.. (e) State in words the interpretation of the partia l derivative L*/r. (f) Use Cramer's rule to solve for L*/r, e xplic itly. Is the sign of this comparative staticgreater than zero? Explain, and show work