Download Algebra 2 300 Section 3.4: Linear Programming Notes: Day #3

Algebra 2 300
Section 3.4: Linear Programming Notes: Day #3
Pages #135-141
1. Your factory makes fruit filled breakfast bars and granola bars. For each case of breakfast
bars, you make $40 profit. For each case of granola bars, you make $55 profit. The table below
show the number of machine hours and labor hours needed to produce one case of each type of
snack bar. It is also shows the maximum number of hours available.
Production Hours
Machine Hours
Labor Hours
Breakfast Bars
2
5
Granola Bars
6
4
Maximum Hours
150
155
a. Define your variables.
b. Write an equation that represents the profit. (Objective Function)
c. Write a system of inequalities that represents the constraints.
d. Sketch the graph of the constraints (feasible region).
e. Label and calculate the corner points.
f. How many cases of each product should you make to maximize the profit?
Algebra 2 300
Section 3.4: Linear Programming Notes: Day #3
Pages #135-141
2. The DHS Bowling club has arranged to earn some extra money by cleaning up Woodland
Park. The Parks & Rec. Department has agreed to pay each old member of the club $10 and
each new member $8 for their services. (The old members have more experience at cleaning
parks.)
a. Define the variables.
b. Write the objective function expressing the dollars the club earns in terms of the number of old
and new members who work.
c. The following factors restrict the numbers of students who can work:
i. Both the numbers of old and new members are non-negative.
ii. The club has at most 9 old members and at most 8 new members who can work.
iii. The department will hire at least 6 students, but no more than 15.
iv. There must be at least 3 new members.
v. The number of new members must be at least half the number of old members.
vi. The number of new members must be less than or equal to 3 times the number of old
members.
d. Graph the system of inequalities and label the corner points.
Algebra 2 300
Section 3.4: Linear Programming Notes: Day #3
Pages #135-141
e. Based on your graph, is it feasible to have no old members at all? Explain.
f. Calculate the corner points.
g. What numbers of old and new members would earn the maximum feasible amount? What is
that amount?
h. What numbers of old and new members would earn the minimum feasible amount? What is
that amount?