3.4b: Linear Programming ~ Application
There are some things you learn best in
calm, and some in storm.
Steps to Linear Programming ~ Application
1) Define the two variables.
2) Write the constraint equations and objective function.
4) Graph the constraints and identify the feasible region.
5) Determine the vertices of the feasible region.
6) Evaluate the objective function at each vertex to
determine maximum and/or minimum values.
Linear Programming ~ Application
Ex1) A furniture manufacturer can make from 30 to 60 tables a day and
from 40 to 100 chairs a day. It can make at most 120 units in one day.
The profit on a table is $150, and the profit on a chair is $65. How many
tables and chairs should they make per day to maximize profit? How
much is the maximum profit?
1) Define the variables.
2) Write the constraints and
objective function.
Linear Programming ~ Application
30  x  60

40  y  100
 x  y  120

3) Graph the constraints.
P = 150x + 65y
4) Find the coordinates of
each vertex.
5) Evaluate the objective
function at each vertex.
Linear Programming ~ Application
In order to ensure optimal health, a lab technician needs to feed the rabbits a
daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates,
and 4 g of protein. But the rabbits should be fed no more than five ounces of
food a day.
Rather than order rabbit food that is custom-blended, it is cheaper to order Food
X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat,
12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce.
Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per
ounce, at a cost of $0.30 per ounce.
1) Define the variables.
2) Write the constraints and objective function.
Linear Programming ~ Application
8 x  12 y  24
12 x  12 y  36


2 x  y  4
 x  y  5
3) Graph the constraints.
C = 0.2x + 0.3y
4) Find the coordinates of
each vertex.
5) Evaluate the objective
function at each vertex.
3.4b: Linear Programming ~ Application
Homework: #11,14-22 even
*#20 in class!
There are some things you learn best in
calm, and some in storm.