Chapter 8.6, Problem 23PE

A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $\text{\$}120$ from the grower. Small trees cost the nursery $\text{\$}80.$ The profit for each large tree sold is $\text{\$}35$ and the profit for each small tree sold is $\text{\$}30.$ The monthly demand is at most $400$ oak trees. Furthermore, the nursery does not want to allocate more than $\text{\$}43,200$ each month on inventory for oak trees.

a. Determine the number of large oak trees and the number of small oak trees that the nursery should have in its inventory each month to maximize profit. (Assume that all trees in inventory are sold.)

b. What is the maximum profit?

c. If the profit on large trees were $\text{\$}50,$ and the profit on small trees remained the same, then how many of each should the nursery have to maximize profit?