A firm has the following inverse demand and total cost relationships: P = 120 – 0.5Q C = 225 + 60Q + Q² a. Determine the quantity (Q) that maximizes profit. b. Calculate P, R, C, AC, and x at the optimal quantity found in part a. c. Determine the quantity (Q) that maximizes total revenue. d. Calculate P, R, C, AC, and x at the optimal quantity found in part c. e. Determine the quantity (Q) that minimizes average cost. f. Calculate P, R, C, AC, and a at the optimal quantity found in part e. Equations: Rules for Optimization Profit Maximization MR = MC Revenue Maximization MR=0 Average Cost Minimization MC-AC or Shortcut: for C=a+bQ+cQ² Q = (a/c)¹/²
Π=R-C R =P*Q AC = C/Q