Suppose a nonlinear price discriminating monopolist faces an inverse demand​ curve: Upper P equals 120 minus Upper Q​, and can set three prices depending on the quantity a consumer purchases. The​ firm's profit​ is: pi equals p 1 Upper Q 1 plus p 2 (Upper Q 2 minus Upper Q 1 )plus p 3 (Upper Q 3 minus Upper Q 2 )minus m Upper Q 3​, where p 1 is the high price charged on the first units Upper Q 1 ​(first block) and p 2 is a lower price charged on the next (Upper Q 2 minus Upper Q 1 )units and p 3 is the lowest price charged on the (Upper Q 3 minus Upper Q 2 )remaining units. Upper Q 3 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 1​, p 2​, and p 3​, and the​ firm's profits.