Holiday Tree Class Fundraiser

The student will determine optimal values in problem situations by identifying

constraints and using linear programming techniques.

Scenario:

Help the 4H club maximize their profits from growing and selling fir trees.

A 4-H club plans to grow Christmas trees as a class project. There is a 1200 square foot plot of land available at their school to grow balsam fir and Douglas fir trees. The profit for each balsam fir tree is $15 and for each Douglas fir $19. A balsam fir requires 10 square feet of space and 6 pounds of fertilizer. A Douglas fir requires 12 square feet of space and 4 pounds of fertilizer. There are only 576 pounds of fertilizer available. Determine the number of each type of fir tree the club should grow to maximize their profit. First, organize your data:

b) What is the objective function?

c) List your constraints.

.

d) Graph the constraints using Desmos.

e) Complete the following chart.

f) How many Balsam firs and Douglas firs would they have to sell for a maximum profit?

Answer in a complete sentence.

g) What is the maximum profit? Write your answer in a complete sentence.

h) Due to the appearance of Balsam firs in the blockbuster movie Evil Tree, demand for Balsams has skyrocketed. You now are able to make $21 per Balsam. How will this affect the number of each tree planted?

Explain your reasoning:  How many of each type of tree will the 4-H Club now sell?

Explain the new maximum profit using a summary statement.