Question #$2$

Blue Ray Manufacturer's Limited utilizes statistical analyses to determine the optimal

price for its sales to customers and the effectiveness of their pricing decisions. During

July $2023$ the company was provided with the following demand and cost functions by

a statistical research company:

$P=200-6Q,$ where $P$ is the unit selling price and $Q$ is the quantity of units in thousands

$TC=5Q^2+24Q+15,$ where TC is total costs in thousands of dollars

Required:

$($a$)$ Determine the optimal output at which profit is maximized for July $2023.$

$($b$)$ Find the price that maximizes profit.

$($c$)$ Determine the maximum sales revenue.

$($d$)$ Calculate the maximum profit.