competitive frim has the following production function, q = 6K^2 3L^2 4KL +60K + 34L. Where p is the market price, w is the wage, and r is the rental rate of capital, then:

a. Write down the firm's profit function.

b. Derive the hotelling's lemma

c. Solve for the optimal K and L by assuming P=10, w=2 and r=3

d. Use the Hessian to check the second order conditions