Algebra 2
Chapter 3
Linear Programming: The Christmas Tree Problem
Name
Period
Date
Monica Pety runs a gift shop in which she sells expensive trees at Christmas time. Her supplier, Connie
Furr, charges her $80 for each real tree, and $160 for each artificial tree. She can buy between 20
and 90 real trees, inclusive, but up to 100 artificial trees. Connie can supply anywhere between 50 and
120 trees, total, but requires that the number of artificial trees ordered be at least half the number of
real trees. Monica is hard-up for cash this year, and wants to invest the minimum feasible amount in
trees.
mmm A.
Define the variables:
B.
Write an objective function:
C.
List the system of constraints that Monica must follow:
D.
Graph the feasible region and then find the vertices.
E.
Use your knowledge of the Corner-Point Principle to help Monica decide how many trees
she should buy.
vertices
Final Answer:
cost
Linear Programming Problem: The School Board Dilemma
A school board is investigating various ways of composing the faculty for a proposed new elementary
school. They can hire teachers and aides. The amount of money the school district will have to spend on
salaries each year depends on how many teachers and on how many aides are hired. The Board finds that
the average teacher’s annual salary is $30,000, and the average aide’s annual salary is $15,000.
Suppose the Board finds the following requirements concerning the permissible numbers of teachers and
aides:
i.
The building can accommodate no more than 50 faculty members, total.
ii.
A minimum of 20 faculty members is needed to staff the school.
iii.
The school cannot be run entirely by aides, so there must be at least 12 teachers.
iv.
For a proper teacher-to-aide ratio, the number of teachers must be at least half the
number of aides.
v.
It is impossible to hire a negative number of teachers or aides.
A.
Define the variables: ____________________________
__________________________
B.
Write an objective function: ________________________
C.
List the system of constraints:
Make a graph of teachers vs. aides and then find the vertices of the polygon.
(teachers, aides)
Final Answer:
cost