Suppose that the production function is given by Q = 25L^ 0.5 K6 0.5 . The amount of funds available to purchase the two inputs is R1500, the price of output (Py) is R4 and L and K both sell for R3.

(a) Set up a lagrangian optimization problem and derive the first-order conditions.

(b) How much L and K should the farmer produce to maximize profit?

(c) Find the value of lambda and interpret the results.

(d) Prove that the total revenue is being maximized, that is, show that the determinant is positive.