[1.2] A manufacturer of plastics is planning to blend a new product from four chemical compounds. These compounds are mainly composed of three elements: A, B, and C. The composition and unit cost of these chemicals are shown in the following table: CHEMICAL COMPOUND 1 2 3 4 Percentage A Percentage B Percentage C Cost/kilogram 35 20 15 35 25 65 35 40 40 15 25 30 20 30 20 15 The new product consists of 25 percent element A, at least 35 percent element B, and at least 20 percent element C. Owing to side effects of compounds 1 and 2, they must not exceed 25 percent and 30 percent, respectively, of the content of the new product. Formulate the problem of finding the least costly way of blending as a linear program.
[1.2] A manufacturer of plastics is planning to blend a new product from four chemical compounds. These compounds are mainly composed of three elements: A, B, and C. The composition and unit cost of these chemicals are shown in the following table: CHEMICAL COMPOUND 1 2 3 4 Percentage A Percentage B Percentage C Cost/kilogram 35 20 15 35 25 65 35 40 40 15 25 30 20 30 20 15 The new product consists of 25 percent element A, at least 35 percent element B, and at least 20 percent element C. Owing to side effects of compounds 1 and 2, they must not exceed 25 percent and 30 percent, respectively, of the content of the new product. Formulate the problem of finding the least costly way of blending as a linear program.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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![[1.2] A manufacturer of plastics is planning to blend a new product from four
chemical compounds. These compounds are mainly composed of three
elements: A, B, and C. The composition and unit cost of these chemicals are
shown in the following table:
CHEMICAL COMPOUND
1
2
3
4
35
Percentage A
Percentage B
Percentage C
Cost/kilogram
35
15
25
20
65
35
40
40
15
25
30
20
30
20
15
The new product consists of 25 percent element A, at least 35 percent element
B, and at least 20 percent element C. Owing to side effects of compounds 1 and
2, they must not exceed 25 percent and 30 percent, respectively, of the content
of the new product. Formulate the problem of finding the least costly way of
blending as a linear program.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e902e76-3891-42dc-a8c0-9abe742ed178%2F97061778-4d22-48e8-aa8a-b1f367a95fd2%2Fpghotnh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[1.2] A manufacturer of plastics is planning to blend a new product from four
chemical compounds. These compounds are mainly composed of three
elements: A, B, and C. The composition and unit cost of these chemicals are
shown in the following table:
CHEMICAL COMPOUND
1
2
3
4
35
Percentage A
Percentage B
Percentage C
Cost/kilogram
35
15
25
20
65
35
40
40
15
25
30
20
30
20
15
The new product consists of 25 percent element A, at least 35 percent element
B, and at least 20 percent element C. Owing to side effects of compounds 1 and
2, they must not exceed 25 percent and 30 percent, respectively, of the content
of the new product. Formulate the problem of finding the least costly way of
blending as a linear program.
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