The function of the dependence of total costs (T) on the volume of output (Q) for a company operating in conditions of perfect competition is described by the formula:

= 2Q² + 6Q + 10

a. Determine the production output that maximizes the profits of the company, and the amount of profit itself, if the unit price of its products is $ 46.

b. The state imposes a lump sum tax of $ 100 on this company. Will the volume of output maximizing the profit of the company and the amount of profit, if the price of the product is still equal to $ 46, change in this case? Prove your point.

c. Let the state instead of a lump-sum tax introduce a quantitative tax on the products of a company with a tax rate of t = $ 4. In this case, will the output volume maximizing the profit of the company and the amount of profit change? If so, how much?