Consider a production function of two inputs, labor and capital, given by Q = (L + K)2. The marginal products associated with this production function

Consider a production function of two inputs, labor and capital, given by Q = (ˆšL + ˆšK)2. The marginal products associated with this production function are as follows:

Let w = 2 and r = 1.
a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q.
b) Find the equation of the firm's long-run total cost curve.
c) Find the equation of the firm's long-run average cost curve.

MP1 = [L + K*]L- MPx = [L+ K+jK-+