Noah and Naomi produce both garden benches and garden chairs; they are price takers in both markets.

Question:

Noah and Naomi produce both garden benches and garden chairs; they are price takers in both markets. Their cost function for garden benches is
(QB, QC) = 50QB+25QC+(QB)2+(QC)2+QBQC
The marginal cost of benches is MBB = 50 +2QB+QC and the marginal cost of chairs is MBC = 25+2QC+QB.
The price of a garden bench, PB, is $120. The price of a garden chair, PC, is $90.
What are Noah and Naomi's profit-maximizing sales quantities of benches and chairs?