a perfectly competitive firm produces output y using two factors of production(inputs), labour L and capital L. The firm's production function is f(L,k) = (L^0.5 + K^0.5)^2 the wage rate is w =9 and the rental price of capital is r= 1

1. find the long run equilibrium price p in this market.
2. suppose in the short run, capital is fixed at k=1. the output price in the short run is p=3. Find the firm's profit maximising output in the short run