Chapter 1, Problem 81RE

Agriculture the number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees planted on an acre of land, then each tree produce 900 - 9n apples, so the number of applesproduced per acre is A(n) = n(900 - 9n) How many trees should be planted per acre to obtain the maximum yield of apples?

Renting Paddleboats An enterprise rents out paddleboats for all-day use on a lake. The owner knows that he can rent out all 27 of his paddleboats if he chargers 1 for each rental. He also knows that he can rent out only 26 if he chargers 2 for each rental and that, in general, there will be 1 less paddleboat rental for each extra dollar that he charges per rental. a. What would the owners total revenue be if he charged 3 for each paddleboat rental? b. Use a formula to express the number of rentals as a function of the amount charged for each rental. c. Use a formula to express the total revenues as a function of the amount charged for each rental. d. How much should the owner charge to get the largest total revenue?