Interior Ltd. produces a single product. The company has employed the services of a statistical firm to develop cost functions that will assist in arriving at the optimal price that will enable the company to maximize profits. During December 2021, you were provided with the following demand and costs functions for the product:

Demand function: P=60+2Q, where P is the unit selling price and Q is quantity of unit in

thousands. Cost function: TC= 3Q² - 2Q + 200, where TC is total costs in thousands of dollars.

Required:

1. Find the output at which profit is maximized.
2. Find the optimal price that maximizes profit.
3. Determine the optimal sales revenue
4. Calculate the maximum profit