The government imposes a tax of T dollars per item sold. The producers of the item react by raising the price to p dollars per item to consumers, which reduces the quantity of items sold to q thousand. We have

p = 50 + 0.2T

q = 10 − T .

(a) What is the tax that maximizes the tax revenue collected by the government?
(b) What is that maximum tax revenue?
(c) With the tax that maximizes tax revenue, what is the producers’ revenue after taxes?
(d) What is the producers’ revenue with no tax?