1. 2-7 Linear Programming
Pre Calc A

2. Vocabulary
Feasible Region
Constraints
Minimum
maximum

3. Steps to Solve Linear Programming Problems
Define variables
Write the profit equation
Write the constraints as a system of inequalities
Graph the system
Find the coordinates of the vertices of the feasible region
Substitute coordinates into the profit equation
Find the minimum and maximum

4. Ex 17:
Myra’s candy factory packages bags of mixed nuts. Myra has 75 lbs of cashews and 120 lbs of peanuts. They are to be mixed in 1 lb packages in the following way: a low grade package contains 4 oz of cashews and 12 oz of peanuts and a high grade package contains 8 oz of peanuts and 8 oz of cashews. A profit of $0.35 per package will be made on the low grade mixture and a profit of $0.55 will be made on the high grade mixture. How many packages of each mixture should Myra make to obtain maximum profit?

5. Ex 17 cont: x = y = P(x) = Constraints: Low grade Mix High Grade Mix
Maximum available
Cashews
Peanuts

6. Graph

7. Find the minimum and maximum
(x, y)
.35x + .55y
P(x, y)
Final answer: