The following total cost and inverse demand functions (in dollars) are given for a firm: 1 TC (q) = 9-q +39 and_p(q) = 84 - q. (a) For what value(s) of q is the profit maximized? What is the maximum profit? (b) If the government sets a tax of St per unit produced, how many units should be produced (in terms of t) by the firm in order to maximize the profit? (c) What tax should be set by the government on each unit produced in order that the tax revenue received by the government be maximized? (Hint: The tax revenue is given by Stq if St is the tax received per unit produced. Thus the government needs to maximize the function T(t) profit-maximizing output found in (b).) = tq where q is the 9