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8. One bag of "Fertilizer A" contains 2 units of phosphorus, 5 units of nitrogen, and 3 units of potassium. One bag of "Fertilizer B" contains 3 units of phosphorus, 4 units of nitrogen, and 6 units of potassium. One bag of "Fertilizer C" contains 5 units of phosphorus, 3 units of nitrogen and 4 units of potassium. A gardener needs to apply at least 75 units of phosphorus, at least 95 units of nitrogen, and at least 80 units of potassium. The price of one bag is $6 for Fertilizer A. $5 for Fertilizer B, and $8 for Fertilizer C. (a) formulate the problem and use the simplex method to determine how many bags of each fertilizer the gardener should purchase in order to meet the above requirements for the lowest possible price; note that the answers must be positive integers minimize subject to: = 6x₁ + 5+ ² 823 2+₁+34 1 523 * Fertilizer A-0 Write the answer in the box below 275 295 80 5 +₁1 44₂ 2 3x, 1642 423) X, , Xъ, X3 373. (b) what is that minimum total price? Write the answer in the box below RUBB 20 X2=22.7273 x3=1.3636 Fertilizer B=22 Fertilizer = 1 124.5455 (c) if all fertilizer is used and applied to the soil in the garden, then will excess amounts of any one of the essential substances (phosphorus, nitrogen, potassium) be applied? if so, which one(s) and in what amount(s)?

8. One bag of "Fertilizer A" contains 2 units of phosphorus, 5 units of nitrogen, and 3 units of potassium. One bag of "Fertilizer B" contains 3 units of phosphorus, 4 units of nitrogen, and 6 units of potassium. One bag of "Fertilizer C" contains 5 units of phosphorus, 3 units of nitrogen and 4 units of potassium. A gardener needs to apply at least 75 units of phosphorus, at least 95 units of nitrogen, and at least 80 units of potassium. The price of one bag is $6 for Fertilizer A. $5 for Fertilizer B, and $8 for Fertilizer C. (a) formulate the problem and use the simplex method to determine how many bags of each fertilizer the gardener should purchase in order to meet the above requirements for the lowest possible price; note that the answers must be positive integers minimize subject to: = 6x₁ + 5+ ² 823 2+₁+34 1 523 * Fertilizer A-0 Write the answer in the box below 275 295 80 5 +₁1 44₂ 2 3x, 1642 423) X, , Xъ, X3 373. (b) what is that minimum total price? Write the answer in the box below RUBB 20 X2=22.7273 x3=1.3636 Fertilizer B=22 Fertilizer = 1 124.5455 (c) if all fertilizer is used and applied to the soil in the garden, then will excess amounts of any one of the essential substances (phosphorus, nitrogen, potassium) be applied? if so, which one(s) and in what amount(s)?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
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Please check my answers and need help on c
8. One bag of "Fertilizer A" contains 2 units of phosphorus, 5 units of nitrogen, and 3 units of potassium. One bag of "Fertilizer B" contains 3 units of phosphorus, 4 units of nitrogen, and 6 units of potassium. One bag of "Fertilizer C" contains 5 units of phosphorus, 3 units of nitrogen. and 4 units of potassium. A gardener needs to apply at least 75 units of phosphorus, at least 95 units of nitrogen, and at least 80 units of potassium. The price of one bag is $6 for Fertilizer A, $5 for Fertilizer B, and $8 for Fertilizer C. (a) formulate the problem and use the simplex method to determine how many bags of each fertilizer the gardener should purchase in order to meet the above requirements for the lowest possible price; note that the answers must be positive integers minimize P-64, +54 +82₂ +542823 subject to: 2+ + 341 527) 2 ,1 ۹۷* 37,164223 X, , Xъ, X3 Write the answer in the box below X₁ = 0 Fertilizer A-0 x2=22.7273 275 295 80 (b) what is that minimum total price? Write the answer in the box below 3737 20 x3=1.3636 Fertilizer = 22 124.5455 Fertilizer = 1 (c) if all fertilizer is used and applied to the soil in the garden, then will excess amounts of any one of the essential substances (phosphorus, nitrogen, potassium) be applied? if so, which one(s) and in what amount(s)?
Transcribed Image Text:8. One bag of "Fertilizer A" contains 2 units of phosphorus, 5 units of nitrogen, and 3 units of potassium. One bag of "Fertilizer B" contains 3 units of phosphorus, 4 units of nitrogen, and 6 units of potassium. One bag of "Fertilizer C" contains 5 units of phosphorus, 3 units of nitrogen. and 4 units of potassium. A gardener needs to apply at least 75 units of phosphorus, at least 95 units of nitrogen, and at least 80 units of potassium. The price of one bag is $6 for Fertilizer A, $5 for Fertilizer B, and $8 for Fertilizer C. (a) formulate the problem and use the simplex method to determine how many bags of each fertilizer the gardener should purchase in order to meet the above requirements for the lowest possible price; note that the answers must be positive integers minimize P-64, +54 +82₂ +542823 subject to: 2+ + 341 527) 2 ,1 ۹۷* 37,164223 X, , Xъ, X3 Write the answer in the box below X₁ = 0 Fertilizer A-0 x2=22.7273 275 295 80 (b) what is that minimum total price? Write the answer in the box below 3737 20 x3=1.3636 Fertilizer = 22 124.5455 Fertilizer = 1 (c) if all fertilizer is used and applied to the soil in the garden, then will excess amounts of any one of the essential substances (phosphorus, nitrogen, potassium) be applied? if so, which one(s) and in what amount(s)?
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