3, Assume that the ice cream industry is perfectly competitive. Each firm producing ice cream must hire an operations manager. There are only 50 operations managers that display extraordinary talent for producing ice cream; there is a potentially unlimited supply of operations managers with average talent. Firms that hire talented operations managers have a long-run total cost LTCT=200+2q?, marginal cost LMCr=4q, and average cost LATCT=200/q+2q, where q is measured in ice cream cones. Firms that hire average operations managers have a long-run total cost LTCA=200+8q?, marginal cost LMCA=16q, and average cost LATCA=200/q+8q. (a) Find the quantity q that minimizes LATCT, and the value of LATCr at that quantity. (b) Find the quantity q that minimizes LATCA, and the value of LATCA at that quantity. (C) Suppose the market demand for ice cream is given by Q=9450-100P where Q is measured in ice cream cones. If all 50 firms with talented managers enter the market (no firms with average managers are in the market), if these firms minimize LATCr, and if these firms charge only their cost, how much ice cream will be demanded? Can these firms supply the market? (d) ^Suppose these firms (still with no competition from average firms) decide to charge the market clearing price. How many of the 50 firms will enter, what will that price be, and what quantity Q will they sell in equilibrium? (Hint: first derive the market supply curve.) (e) Given the above, will firms with average operations managers enter the market? What will be the equilibrium price? How many firms of each type will enter the market, and what quantity will each type supply