Suppose that it costs a company y = a + bx dollars to produce x units per week. It can sell x units per week at a price of P = c - ex dollars per unit. Each of a, b, c, and e represents a positive constant. 

(a) What production level maximizes the profit? 

(b) What is the corresponding price? 

(c) What is the weekly profit at this level of production? 

(d) At what price should each item be sold to maximize profits if the government imposes a tax of t dollars per item sold? Comment on the difference between this price and the price before the tax.