A pet food factory blends four ingredients into three types of pet food: value, premium, and basic.
Question:
A pet food factory blends four ingredients into three types of pet food: value, premium, and basic. The maximum quantities available of each ingredient and the costs per ounce are given in the table below:
Ingredient | Maximum pounds available per day | Cost per ounce |
1 | 5,000 | $0.5625 |
2 | 2,400 | $0.4375 |
3 | 4,000 | $0.7500 |
4 | 1,500 | $0.3750 |
The operations manager has placed limits on the component to be added to each blend. The limits and the selling price for each blend are shown in the table below:
Variant | Component Specifications | Selling Price per pound |
Value | Not less than 40% of 1 | $12.00 |
Value | Not more than 20% of 2 | $12.00 |
Value | Not less than 30% of 3 | $12.00 |
Premium | Not less than 40% of 3 | $18.00 |
Basic | Not more than 50% of 2 | $10.00 |
Basic | Not less than 10% of 1 | $10.00 |
The marketing manager wants to produce at least 3,000 pounds of each variant of pet food.
1.1 Develop a linear programming model to help the company determine the best mix to produce to maximize profits.
1.2 Determine the optimal solution and recommend a strategy for producing pet food.
Operations Management Creating Value Along the Supply Chain
ISBN: 978-0470525906
7th Edition
Authors: Roberta S. Russell, Bernard W. Taylor