Linear Programming Review w answers.notebook - Ms. Carrigg's ...

Linear Programming Review w answers.notebook
October 24, 2011
Do Now: Find the max and min values of the objective function
subject to the given constraints.
1.)
y
10
9
8
7
6
5
4
3
2
1
x
­2 ­1 0 1 2 3 4 5 6 7 8 9 10
­1
­2
y
6
2.)
5
4
3
2
1
x
­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6
­1
­2
­3
­4
­5
­6
1

Linear Programming Review w answers.notebook
October 24, 2011
Project Information
y
6
5
4
3
2
1
x
­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6
­1
­2
­3
­4
­5
­6
2

Linear Programming Review w answers.notebook
October 24, 2011
1.) A toy manufacturer wants to minimize her cost for producing
two lines of toy airplanes. Because of the supply of materials, no
more than 40 Flying Bats can be built each day, and no more than
60 Flying Falcons can be built each day. There are enough workers
to build at least 70 toy airplanes each day. It costs $12 to
manufacture a Flying Bat and $8 to build a Flying Falcon. What is
the minimum possible cost each day?
3

Linear Programming Review w answers.notebook
October 24, 2011
2.) A seafood restaurant owner orders at least 50 fish. He cannot use more
than 30 amberjack or more than 35 flounder. Amberjack costs $4 each and
flounder costs $3 each. How many of each fish should be used to minimize
his cost?
4

Linear Programming Review w answers.notebook
October 24, 2011
3.) Fly­High Airlines sells business class and tourist class seats for its
charter flights. To charter a plane at least 5 business class tickets must be
sold and at least 9 tourist class tickets must be sold. The plane does not
hold more than 30 passengers. Fly­High makes $40 profit for each
business class ticket sold and $45 profit for each tourist class ticket sold.
In order for Fly­High Airlines to maximize its profits, how many tourist
class seats should they sell?
5

Linear Programming Review w answers.notebook
October 24, 2011
4.) A bakery is making whole­wheat bread and apple bran muffins. For
each batch of bread they make $35 profit. For each batch of muffins they
make $10 profit. The bread takes 4 hours to prepare and 1 hour to bake.
The muffins take 0.5 hours to prepare and 0.5 hours to bake. The
maximum preparation time available is 16 hours. The maximum baking time
available is 10 hours. How many batches of bread and muffins should be
made to maximize profits?
6

Linear Programming Review w answers.notebook
October 24, 2011
You are a stenciling wooden boxes to sell at a fair. It takes
you 2 hours to stencil a small box and 3 hours to stencil a
large box. You make a profit of $10 for a small box and
$20 for a large box. If you have no more than 30 hours
available to stencil and want at least 12 boxes to sell, how
many of each size box should you stencil to maximize
your profit.
y
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
x
­1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
­1
7

Linear Programming Review w answers.notebook
October 24, 2011
8