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(Multiplant Monopoly) Consider a monopoly that faces the demand curve P=120-3Q, where Q =q1+ q2 is the total output from the two plants operated by the firm. The two plants are characterized by the total cost functions TC(q1)=10q1+10(q1)^2 and TC(q2)=60q2+2.5(q2)^2. q respectively.
(a) Find the total output produced by the monopoly in equilibrium and the equilibrium price.
(b) What is the output produced by the monopoly in each of its two plants?
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