I
Linear Programming
Follow the Leader
Candy Factory
Your candy factory is making chocolate-covered peanuts and
chocolate-covered pretzels. For each case of peanuts, you make
$40 profit. For each case of pretzels, you make $55 profit. The
table below shows the number of machine hours needed to
produce one case of each type of candy. It also shows the
maximum number of hours available. How many cases of each
product should you make to maximize profits?
Production Hours
Machine Hours
M a n Hours
Variables
X=
Y=
Peanuts Pretzels
2
6
5
4
Objective Quantity
Constraints
Maximum Hours
1 5 0
1 5 5
Vertices
Bicycles
A manufacturer can show a profit on a bicycle of $6
and a profit on a tricycle of $4. Department A
requires 3 hours to manufacture the parts for a
bicycle and 4 hours for tricycle. Department B
takes 5 hours to assemble a bicycle and 2 hours to
assemble a tricycle. How many bicycles and
tricycles should be produced to maximize the
profit if the total time available in department A is
450 hours and in B is 400 hours?
Variables
x=
Y=
Objective Quantity
Constraints
Vertices
Light Fixtures
• A company makes two models of light fixtures, A
and B, each of which must be assembled and
packed. The time required to assemble model A is
12 minutes, and model B takes 18 minutes. It takes
2 minutes to package model A and 1 minute to
package model B. Each week there are available
240 minutes of assembly time and 20 minutes for
packing. If model A sells for $1.50 and model B
sells for $1.70, how many of each model should be
made to obtain the maximum weekly income?
What is the maximum weekly income?
• Variables
• X=
• Y=
Objective Quantity
Constraints
Vertices
The Lumber Yard
•
The Champion Lumber Company converts logs into lumber or plywood.
In a given week, the total production cannot exceed 800 units, of which
200 units of lumber and 300 units of plywood are required by regular
customers. The profit on a unit of lumber is $20, and the profit on a unit
of plywood is $30. What combination of lumber and plywood would yield
the maximum profit?
•
•
•
Variables
X=
Y=
Objective Quantity
Constraints
Vertices
Bird Houses
•
Bob and Betty make birdhouses and mailboxes in their craft shop. Each
birdhouse requires 3 hours of work from Bob and 1 hour of work from
Betty. Each mailbox requires 4 hours of work from Bob and 2 hours of
work from Betty. Bob cannot work more than 48 hours each week and
Betty cannot work more than 20 hours each week. If each birdhouse
sells for $12 and each mailbox sells for $20, how many of each should
they make to maximize their profits?
•
•
•
Variables
X=
Y=
Objective Quantity
Constraints
Vertices