Question: (a) A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x + 0.25x2 dollars. Find the production level that maximizes profits.
(b) A tax of $10 per unit is imposed. What is now the optimal production level?
(c) Answer the question in (b) if the sales price per unit is p, the total cost of producing and selling x units is αx + βx2, and the tax per unit is t.