Suppose a nonlinear price discriminating monopoly can set three prices, depending on the quantity a consumer purchases. The firm's profit is IT = P1 (Q1 ) + P2 (Q2 1) +P3 ( 3 2) - me 3 where p1 is the high price charged on the first Q, units (first block), p2 is a lower price charged on the next Q2 - Q1 units, p3 is the lowest price charged on the Q3 - Q2 remaining units, Q, is the total number of units actually purchased, and m =$30 is the firm's constant marginal and average cost. Use calculus to determine the profit-maximizing p1, P2, and P3. Let demand be p = 270 - Q. The profit-maximizing prices for the nonlinear price discriminating monopoly are P1 =$ P2 =$ and P3 =$ (Enter numeric responses using real numbers rounded to two decimal places.)