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An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10e. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X1 X2 S2 S3 2.5 0. 7 4.5 3 1. 10 10 - 60 -67 There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual. When pivoting on the second row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. When pivoting on the third row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and (Round to the nearest tenth as needed.) grams of grain.

An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10e. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X1 X2 S2 S3 2.5 0. 7 4.5 3 1. 10 10 - 60 -67 There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual. When pivoting on the second row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. When pivoting on the third row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and (Round to the nearest tenth as needed.) grams of grain.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10e. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X1 X2 S2 S3 2.5 7 4.5 3 1. 10 1 10 - 60 - 67 There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual. When pivoting on the second row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. When pivoting on the third row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. (Round to the nearest tenth as needed.)
Transcribed Image Text:An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10e. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X1 X2 S2 S3 2.5 7 4.5 3 1. 10 1 10 - 60 - 67 There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual. When pivoting on the second row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. When pivoting on the third row of the dual, the mixture would contain 0 grams of soybean meal, grams of meat byproducts, and grams of grain. (Round to the nearest tenth as needed.)
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