2. • A type of optimization process.
▫ Optimization – finding the max or min
value of some quantity
• Optimizes an objective function subject
to a system of linear inequalities called
constraints.
• The graph of the system of constraints is
called the feasible region.
• Used in many real-life situations.
What is Linear Programming?
3. The Corner-Point Principle
A maximum or minimum value of a linear
equation P = Ax + By, if it exists, will occur at a
corner point of the feasible region.
So, to find max/min:
1. Write the objective function
2. Write the constraints (system of inequalities)
3. Graph feasible region
4. Find corner points
5. Plug them in to find the max/min
4. Your factory makes fruit bars and granola bars.
For each case of fruit bars, you make $40
profit. For each case of granola bars, you
make $55 profit. The table below shows the
number of machine hours and labor hours
needed to produce one case of each type. It
also shows the max number of hours
available. How many cases of each should be
made to maximize profit?
Example 1
Production
Hours
Fruit Bars Granola Bars
Maximum
Hours
Machine Hours 2 6 150
Labor Hours 5 4 155
5.
6. Example 2
• Every day Rhonda needs a supplement of 4 mg of
vitamin A, 11 mg of vitamin B, and 100 mg of vitamin
C. Either of two brands of vitamins can be used:
Brand X at $0.06 per pill of Brand Y at $0.08 per pill.
The pills supply the amount of each vitamin shown in
the chart. How many pills of each brand should she
take each day to satisfy the minimum daily need most
economically?
Brand X Brand Y Minimum Daily Need
Vitamin A 2 mg 1 mg 4 mg
Vitamin B 3 mg 4 mg 11 mg
Vitamin C 25 mg 50 mg 100 mg
Cost per pill 6 cents 8 cents
