Martin$$s Enterprise has been experiencing difficulties with respect to the competitiveness of the price that it charges to consumers. In January $2021,$ a market research team used demand and supply information to arrive at the following demand and cost functions:

P$=200-4$Q; where P is the unit selling price and Q is the quantity of units in thousands.

TC$=6$Q$2+30$Q $+350$; where TC is total costs in thousands of dollars.

Required:

$($a$)$ Determine the output level that would maximize profits for Martin$$s Enterprise.

$($b$)$ Compute the optimal price that Martin$$s Enterprise should charge in order to maximize profit.

$($c$)$ Calculate the optimal sales revenue that would maximize profits.

$($d$)$ How much profit would Martin$$s Enterprise make in January $2021?$