1. Pet Food Company
A pet food company wants to find the optimal mix of ingredients, which will minimize the cost of a batch of food, subject to constraints on nutritional content. There are two ingredients, P1 and P2. P1 costs $5/lb. and P2 costs $8/lb. A batch of food must contain no more than 400 lbs. of P1 and must contain at least 200 lbs. of P2. A batch must contain a total of at least 500 lbs. What is the optimal (minimal cost) mix for a single batch of food?
Linear Programming

2. Pet Food Company – Linear Equations
Linear Programming

3. Pet Food Company – Graph Solution
Linear Programming

4. Pet Food Company – Graph Solution Constraint 1
Linear Programming

5. Pet Food Company – Graph Solution Constraint 1
Linear Programming

6. Pet Food Company – Graph Solution Constraint 2
Linear Programming

7. Pet Food Company – Graph Solution Constraint 1 & 2
Linear Programming

8. Pet Food Company – Graph Solution Constraint 3
Linear Programming

9. Pet Food Company – Graph Solution Constraint 1, 2 & 3
Linear Programming

10. Pet Food Company – Solve Linear Equations
Linear Programming

11. Pet Food Company – Graph Solution
Linear Programming

12. Pet Food Company – Solve Linear Equations
Linear Programming

13. Pet Food Company – Solve Linear Equations
Linear Programming

14. Pet Food Company – Graph Solution
Optimal Point
(300, 200)
Linear Programming

15. Pet Food Company – Slack/ Surplus Calculation
Linear Programming

16. Pet Food Co. – Linear Equations Slack/ Surplus Variables
Min
5P1 + 8P2 + 0S1 + 0S2 + 0S3
s.t.
1P S = 400
1P S = 200
1P1 + 1P S3 = 500
P1, P2, S1 ,S2 ,S3 >= 0
Linear Programming

17. Pet Food Co. – Slack Variables
For each ≤ constraint the difference between the RHS and LHS (RHS-LHS). It is the amount of resource left over.
Constraint 1; S1 = 100 lbs.
Linear Programming

18. Pet Food Co. – Surplus Variables
For each ≥ constraint the difference between the LHS and RHS (LHS-RHS). It is the amount bt which a minimum requirement is exceeded.
Constraint 2; S2 = 0 lbs.
Constraint 3; S3 = 0 lbs.
Linear Programming