The demand equation for a company is P = 200 -3x And the cost function is C(x) = 75 + 80x – x2 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 R4 per unit quantity produced, determine the new price that maximizes the profit.

The demand equation for a company is P = 200 -3x

And the cost function is C(x) = 75 + 80x – x2

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 R4 per
unit quantity produced, determine the new price that maximizes the
profit.