Noah and Naomi can produce garden benches, garden chairs or both; they are price takers in both mark

Noah and Naomi can produce garden benches, garden chairs or both; they are price takers in both markets. Their cost function for garden benches is:

C_B(Q_BQ_C)= 80Q_B + (Q_B)²⁺Q_BQ_C

and Marginal Cost = MC_B=80+2Q_B+Q_C

Cost Function for Garden Chairs: C_C(Q_BQ_C)=25Q_C+(Q_c)²+Q_CQ_B

Marginal Cost: MC_C=25+2Q_C+Q_B

The price of a garden bench P_B=$120, the price of a garden chair P_C=$60

a.  What are Noah and Naomi's profit-maximizing sales quantities of benches and chairs. Round to one decimal place and show work for Benches and Chairs.

b.  What is the profit-maximizing quantities if the price of benches increases to $135? Round your answers to 1 decimal place and show work.