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40. A farmer needs at least 360 kg of nitrogen, 257 kg of phosphate and 250 kg of potassium to fertilize his land. His supplier has two types of fertilizer. One kg of fertilizer I contains 30 g of nitrogen, 50 g of phosphate and 10 g of potassium and costs €0.70 per kg. One kg of fertilizer II contains 40 g of nitrogen, 20 g of phosphate and 40g of potassium and costs €1 per kg. (a) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? (b) How much will the farmer have to pay to his supplier then? The supplier intends to increase the price of the first fertilizer. He does not yet know precisely by how much, but the new price per kilogram will be at most €0.80. The farmer wants to be prepared and does a number of calculations. Call p the price per kilogram (in €) of the first fertilizer (where 0.70 ≤p ≤ 0.80, as said before). (c) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? Your answer may depend on the value of p. (d) Express the total cost (in €) of the farmer in terms of p.

40. A farmer needs at least 360 kg of nitrogen, 257 kg of phosphate and 250 kg of potassium to fertilize his land. His supplier has two types of fertilizer. One kg of fertilizer I contains 30 g of nitrogen, 50 g of phosphate and 10 g of potassium and costs €0.70 per kg. One kg of fertilizer II contains 40 g of nitrogen, 20 g of phosphate and 40g of potassium and costs €1 per kg. (a) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? (b) How much will the farmer have to pay to his supplier then? The supplier intends to increase the price of the first fertilizer. He does not yet know precisely by how much, but the new price per kilogram will be at most €0.80. The farmer wants to be prepared and does a number of calculations. Call p the price per kilogram (in €) of the first fertilizer (where 0.70 ≤p ≤ 0.80, as said before). (c) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? Your answer may depend on the value of p. (d) Express the total cost (in €) of the farmer in terms of p.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 46E
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could you please write it with pen and paper? i appreciate it

40. A farmer needs at least 360 kg of nitrogen, 257 kg of phosphate and 250 kg of potassium to fertilize his land. His supplier has two types of fertilizer. One kg of fertilizer I contains 30 g of nitrogen, 50 g of phosphate and 10 g of potassium and costs €0.70 per kg. One kg of fertilizer II contains 40 g of nitrogen, 20 g of phosphate and 40g of potassium and costs €1 per kg. (a) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? (b) How much will the farmer have to pay to his supplier then? The supplier intends to increase the price of the first fertilizer. He does not yet know precisely by how much, but the new price per kilogram will be at most €0.80. The farmer wants to be prepared and does a number of calculations. Call p the price per kilogram (in €) of the first fertilizer (where 0.70 ≤p ≤ 0.80, as said before). (c) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? Your answer may depend on the value of p. (d) Express the total cost (in €) of the farmer in terms of p.
Transcribed Image Text:40. A farmer needs at least 360 kg of nitrogen, 257 kg of phosphate and 250 kg of potassium to fertilize his land. His supplier has two types of fertilizer. One kg of fertilizer I contains 30 g of nitrogen, 50 g of phosphate and 10 g of potassium and costs €0.70 per kg. One kg of fertilizer II contains 40 g of nitrogen, 20 g of phosphate and 40g of potassium and costs €1 per kg. (a) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? (b) How much will the farmer have to pay to his supplier then? The supplier intends to increase the price of the first fertilizer. He does not yet know precisely by how much, but the new price per kilogram will be at most €0.80. The farmer wants to be prepared and does a number of calculations. Call p the price per kilogram (in €) of the first fertilizer (where 0.70 ≤p ≤ 0.80, as said before). (c) How much of both fertilizers does the farmer have to buy to fertilize his land as cheaply as possible? Your answer may depend on the value of p. (d) Express the total cost (in €) of the farmer in terms of p.
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