Directions: Answer all of the questions fully, being sure to show all necessary work.

(1) A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the grower, and small trees cost the nursery $ 80. The profit for each type of tree is $35 for each large tree sold, and $ 30 for each small tree sold. The monthly demand is at most 400 oak trees. Furthermore, the nursery does not want to allocate more than $43200 each month on inventory for oak trees.

1. (a)Letxbe the number of Large oak trees sold, andybe the number of small oak trees sold. Write the objective function for profit for this scenario:
2. Profit=
3. (b)The sales the nursery makes (and thus the profit they earn) is limited by several factors. For each constraint list a inequality representing the constraints:
4. (i)The number of trees of each type cannot be negative. (This is two seperate ineqaulities.)
5. (ii)The monthly demand (total number of trees sold) is at most 400 oak trees.
6. (iii)The nursery does not want to allocate more than $43200 each month on inventory for oak trees, and each large tree costs the nursery $120 from the grower, and each small tree costs the nursery $ 80.

(c) Graph the system of inequalities represented by the constraints you just found, and shade the feasible region.

1. (d)List all the vertices of the feasible region.
2. (e)Test the objective function at each vertex
3. (f)What is the number of large and small oak trees the nursery should have in inventory to maximize profit?
4. (g)What is the maximum profit?