1. Section 7.5
Linear Programming

2. Objective By following instructions students will be able to:
Solve linear programming problems.
Use linear programming to model and solve real-life problems.

3. Inequalities
Greater than/ Greater than or equal to
shade above
Less than/ Less than or equal to
shade below

4. Example 1:
Find the maximum value of Subject to the following constraints.

5. Example 2:
Find the minimum value of Where , subject to the following constraints.

6. Example 3:
Find the maximum value of Where , subject to the following constraints.

7. U-TRY #1
Find the minimum and maximum values of subject to the following constraints.

8. Example 4:
Find the maximum value of Where , subject to the following constraints.

9. Example 5:
A manufacturer wants to maximize profit for two products. Hot Cheetos yields a profit of $1.50 per bag, and Doritos yields a profit of $2.00 per bag. Market tests and available resources have indicated the following constraints.
The combined production level should not exceed 1200 bags per month.
The demand for Doritos is no more than half the demand for Hot Cheetos.
The product level of Hot Cheetos is less than or equal to 600 bags plus three times the production level of Doritos.

10. Example 6:
The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X costs $0.12 and provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y cost $0.15 and provides 60 calories, 6 units of vitamin A, and 30 units vitamin C. How many cups of each drink should be consumed each day to minimize the cost and still meet the daily requirements?

11. Revisit Objective Did we… Solve linear programming problems?
Use linear programming to model and solve real-life problems?

12. Homework
Pg 541#s 1-39 ODD