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 2,400 $0.4375 3 4,000 $0.7500 4 1,500 $0.3750 2.
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 2,400 $0.4375 3 4,000 $0.7500 4 1,500 $0.3750 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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
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.
Develop a linear programming model to help the company determine the best mix to produce to maximize profits.
Determine the optimal solution and recommend a strategy for producing the pet food.
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