A firm that produce brownies has a production function: F(K,L)= (K^1/2 + L^1/2)^2. (Hint: for this question plugging in w=1 and r=1 sooner than later will save you some time with your algebra).
a?- First, find the optimal amount of capital and labor that this firm should hire if it wants to minimize its cost to produce q units of output.
b. solve for the cost function in terms of quantity q, that your firm is free to choose both labor and capital.
c. What is the firm marginal cost?
d. what is the average total cost??