The demand equation for a company is p = 200 - 3x, and the cost function is C(x) = 75 + 80x - x², 0 ≤ x ≤ 40.

(a) Determine the value of x and the corresponding price that maximize the profit.

(b) If the government imposes a tax on the company of $4 per unit quantity produced, determine the new price that maximizes the profit.

(c) The government imposes a tax of T dollars per unit quantity produced (where 0 ≤ T ≤ 120), so the new cost function is C(x) = 75 + (80 + T )x - x², 0 ≤ x ≤ 40.

Determine the new value of x that maximizes the company’s profit as a function of T. Assuming that the company cuts back production to this level, express the tax revenues received by the government as a function of T. Finally, determine the value of T that will maximize the tax revenue received by the government.