Suppose a nonlinear price discriminating monopolist faces an inverse demand curve: P = 175 - Q, and can set three prices depending on the quantity a consumer purchases. The firm's profit is: IT = P1Q1 + P2 (Q2 - Q1 ) + P3 ( Q3 - Q2) - mQ3, where p, is the high price charged on the first units Q, (first block) and p2 is a lower price charged on the next (Q2 - Q, ) units and p3 is the lowest price charged on the (Q3 - Q2) remaining units. Q3 is the total number of units actually purchased, and m = $50 is the firm's constant marginal and average cost. Using calculus, determine the profit-maximizing values for P, , P2, and p3, and the firm's profits. The profit-maximizing value for (round your answers to the nearest penny) P1 = $ . P2 = $ , and P3 = $ The firm's profit is $ K