The Bartram Bitumen Company has two plants producing bituminous tar for its market in which it has a virtual monopoly because of the remote location of other firms producing bitumi¬ nous tar. The marketing manager has estimated the firm’s demand curve as P = 68.5 - 0 005Q- and the production manager has estimated the monthly cost functions as TC = 5,850 + 1.5Q + 0.005 Q2 for plant A, and TC = 6,250 + 1.2Q + 0.003 Q2 for plant B, where Q represents pounds of tar in all cases.

(a) Please advise Bartram about the profit-maximizing output level from both plants in total.

(b) How much of this output should come from plant A?

(c) What price should Bartram set?

(d) Demonstrate that total contribution would decline if the last 100 units to be produced in plant A could not be produced there because of a breakdown and had to be produced in plant B instead.