1. A firm has the following inverse demand and total cost relationships: P= 120-0.50 C=225 + 600+ 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 o= (a/c)1/2 HI=R-C R=P *Q AC=C/