1. A firm produces two goods, x and y. Due to a government quota, the firm must produce subject to the constraint x y = 42. The firm's total cost function is C(x, y) = 8x 2 xy 12y

2 . Optimize the total cost. 2. Find the critical points of w = 3x 2 2y 3 6xy and determine their type (extreme/ saddle/inflection).

3. Discuss consumer's surplus and producer's surplus graphically.