Spring Time Manufacturers produces a single product and the company is trying to determine the effectiveness of their pricing decisions. As a consultant, you have been asked to develop cost functions that will assist in arriving at the optimal price that will enable the company to maximize profits. During the year, you were provided with the following demand and costs functions for the product:

P = 485-25Q, where P is the unit selling price and Q is quantity of units in thousands.

TC = 5Q² + 95Q + 200, where TC is total costs in thousands of dollars.

Required:

(a)Find the output at which profit is maximized.

(b)Find the optimal price that maximizes profit.

(c)Determine the optimal sales revenue.

(d)Calculate the maximum profit.