A cereal manufacturer wishes to produce 1000 pounds of a cereal that contains exactly 10% fiber, 2% fat, and 5% sugar (by weight). The cereal is to be produced by combining four items of raw food material in appropriate proportions. These four items are named A, B, C, D and they have certain combinations of fiber, fat, and sugar content, and are available at various prices per pound: Item Fiber Fat Sugar Price/lb A 4 LO 5 13 2 B 6 26 4 4 с 12 9 5 1 D 3 8 0 2 The manufacturer wishes to find the amounts of each item to be used to produce the cereal in the least expensive way. Formulate the problem as a linear programming problem.
A cereal manufacturer wishes to produce 1000 pounds of a cereal that contains exactly 10% fiber, 2% fat, and 5% sugar (by weight). The cereal is to be produced by combining four items of raw food material in appropriate proportions. These four items are named A, B, C, D and they have certain combinations of fiber, fat, and sugar content, and are available at various prices per pound: Item Fiber Fat Sugar Price/lb A 4 LO 5 13 2 B 6 26 4 4 с 12 9 5 1 D 3 8 0 2 The manufacturer wishes to find the amounts of each item to be used to produce the cereal in the least expensive way. Formulate the problem as a linear programming problem.
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 cereal manufacturer aims to produce 1000 pounds of a cereal that contains exactly 10% fiber, 2% fat, and 5% sugar by weight. The cereal will be made by combining four raw food materials, named A, B, C, and D, in specific proportions. These items have different combinations of fiber, fat, and sugar content, and are available at varying prices per pound, as shown in the table below:
| Item | A | B | C | D |
|-------|---|---|---|---|
| Fiber | 4 | 6 | 12| 3 |
| Fat | 5 | 26| 9 | 8 |
| Sugar | 13| 4 | 5 | 0 |
| Price/lb | 2 | 4 | 1 | 2 |
The table explains the content percentages for each nutrient (fiber, fat, sugar) for items A, B, C, and D, along with their respective prices per pound.
The manufacturer needs to determine how much of each item should be used to produce the cereal at the lowest cost. This problem should be framed as a linear programming problem.
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