Suppose the two-input production function has corresponding cost function:

C (q, (w1, w2) =1+ (w1, w22q2)

a. Find conditional factor demands

b. is the production function homothetic?

c. draw the marginal and average cost curves for w1 = w2 = 1.

d. Find the profit function π (p, (w1, w2) for all values of p > 0, (w1, w2) > 0