A Monopolist Owns Two Plants in Which to Produce a Product

Multiple Choice

A monopolist owns two plants in which to produce a product which has inverse demand $P =$ $( 770 / 3 ) - 3 Q$ . The monopolist has marginal cost curves of $M C _ { 1 } = 20 + 3 Q _ { 1 }$ and $M C _ { 2 } = 10 + 6 Q _ { 2 }$ in the two plants, respectively. Which of the following represents the optimal outputs in the two plants, $Q _ { 1 }$ and $Q _ { 2 }$ and the market price?

A) $Q _ { 1 } = 170 / 9 ; Q _ { 2 } = 100 / 9 ; P = 500 / 3$ .
B) $Q _ { 1 } = 100 / 9 ; Q _ { 2 } = 170 / 9 ; P = 500 / 3$ .
C) $Q _ { 1 } = 500 / 3 ; Q _ { 2 } = 170 / 9 ; P = 100 / 9$ .
D) $Q _ { 1 } = 500 / 3 ; Q _ { 2 } = 100 / 9 ; P = 170 / 9$ .