A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 5 to 3. The amount of nitrogen must be at least 39 kg. The percent of nitrogen in the three chemicals is 8%,4%,and 5%,respectively. If the three chemicals cost $1.02 $0.86 and $0.66 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 600 kg of the plant food?

A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 5 to 3. The amount of nitrogen must be at least 39 kg. The percent of nitrogen in the three chemicals is 8%,4%,and 5%,respectively. If the three chemicals cost $1.02 $0.86 and $0.66 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 600 kg of the plant food?

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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Question

A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 5
to 3. The amount of nitrogen must be at least 39 kg. The percent of nitrogen in the three chemicals is 8%,4%,and 5%,respectively. If the three chemicals cost $1.02 $0.86 and $0.66 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 600 kg of the plant food?

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