3) Jim is selling sweatshirts on the quad. When he sets the price at $28 per sweatshirt, they sell 200 sweatshirts each week. For every $1 increase in price per sweatshirt, they will sell 4 fewer sweatshirts per week. a) Find the revenue function. Clearly identify your variables Revenue b.) use a method of calculus to maximize the weekly revenue from selling sweatshirts. Determine the number of sweatshirts they must sell, the price, and find the maximum revenue. You must verify that you did find the maximum. (SHOW all work in the space below) Number of sweatshirts Price of the sweatshirt_ Verity (test) you need to state the domain you are using ang test correctly.

The owner of an apartment building has 100 apartments. He has found that if he charges $500 per month he can rent all 100 of them but he rents one fewer apartment for each $25 increase in monthly rent.   a. Write an equation that gives the monthly revenue from the rental of the apartments if he makes x increases of $25 in the rent. b. Find the rent he should charge to maximize the monthly revenue and the number of apartments he will rent by charging this amount. c. Suppose the landlord pays for water, sewer, and electricity at his apartments for a cost of $50 per apartment per month. Write an equation that gives the monthly cost to the landlord after x price increases of $25. d. Write an equation that gives the monthly profit the landlord makes, and the rent he should charge to maximize his monthly profit, and the number of apartments he will rent by charging this amount. e. Explain why you know mathematically your solutions to (2) and (4) are maximum values. f. In a sentence or two…