Suppose a nonlinear price discriminating monopoly can set three prices, depending on the quantity a consumer purchases. The firm's profit is IT = P1 (Q 1 ) + P2 ( Q2 - Q1 ) + P3 ( Q3 - Q2 ) - mQ3, where p, 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 = $50 is the firm's constant marginal and average cost. Use calculus to determine the profit-maximizing p1, P2, and P3. Let demand be p = 150 - 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.)