A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals Il and IIl must be in the ratio of 5 to 2. The amount of nitrogen must be at least 47 kg. The percent of nitrogen in the three chemicals 9% , 2%, and 3%, respectively. If the three chemicals cost $1.03, $0.89, and $0.61 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 750 kg of the plant food? The minimum cost plant food is made wwith ka of chemical I ka of chemical II and ka of chemical III

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Author:Erwin Kreyszig
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A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals Il and III must be in the ratio of 5 to 2. The amount of nitrogen must be at least 47 kg. The percent of nitrogen in the three chemicals is
9%, 2%, and 3%, respectively. If the three chemicals cost $1.03, $0.89, and $0.61 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 750 kg of the plant food?
The minimum cost plant food is made with kg of chemical I,
kg of chemical II, and
kg of chemical III.
Transcribed Image Text:A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals Il and III must be in the ratio of 5 to 2. The amount of nitrogen must be at least 47 kg. The percent of nitrogen in the three chemicals is 9%, 2%, and 3%, respectively. If the three chemicals cost $1.03, $0.89, and $0.61 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 750 kg of the plant food? The minimum cost plant food is made with kg of chemical I, kg of chemical II, and kg of chemical III.
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