The variable cost per unit for the production ofq Winter tires in a given day is

v=18-0.02q+0.00002q^2, 0 less than or equal to q less than or equal to 500

If the demand function for the winter tires is

p=34-0.028q, 0 less than or equal to q less than or equal to 500

(a.) find the daily production level that will result in a maximum profit. (Assume that fixed costs are $100 per day).

(b.) Suppose that Winter Tires are assessed a lump-sum tax that amounts to $4 per day. Treating this tax as a portion of the fixed costs, find the output level that maximizes profit after taxes. What effect does a lump-sum tax have on the optimum output level?

(c.) Suppose that instead of the lump-sum tax, Winter Tires are assessed a windfall profits tax of 8%; i.e., the new profit function is0.92

0.92times the old one. Find the output level that maximizes profit after this tax. What effect does this percentage of profits tax have on the optimal output level?