A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric acid, 75 pounds of nitrogen, and 20 pounds of potash; each barrel of mix B contains 30 pounds of phosphoric acid, 100 pounds of nitrogen, and 30 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 30 pounds of potash; and each barrel of mix D contains 60 pounds of phosphoric acid, 25 pounds of nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 840 pounds of phosphoric acid, 825 pounds of nitrogen, and 740 pounds of potash. How many barrels of each type of food should the farmer mix together supply the necessary nutrients for the field? ... Let x₁ be the number of barrels of Mix A, x₂ be the number of barrels of Mix B, x3 be the number of barrels of Mix C, and x4 be the number of barrels of Mix D. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution is x₁ = X3 =, and x4 = . (Simplify your answer.) OB. There are multiple combinations of how the barrels should be filled. The combinations are obtained from the equations x₁ = , and x4 = t for sts. (Simplify your answer. Type an expression using t as the variable.) OC. There is no solution.
A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric acid, 75 pounds of nitrogen, and 20 pounds of potash; each barrel of mix B contains 30 pounds of phosphoric acid, 100 pounds of nitrogen, and 30 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 30 pounds of potash; and each barrel of mix D contains 60 pounds of phosphoric acid, 25 pounds of nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 840 pounds of phosphoric acid, 825 pounds of nitrogen, and 740 pounds of potash. How many barrels of each type of food should the farmer mix together supply the necessary nutrients for the field? ... Let x₁ be the number of barrels of Mix A, x₂ be the number of barrels of Mix B, x3 be the number of barrels of Mix C, and x4 be the number of barrels of Mix D. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution is x₁ = X3 =, and x4 = . (Simplify your answer.) OB. There are multiple combinations of how the barrels should be filled. The combinations are obtained from the equations x₁ = , and x4 = t for sts. (Simplify your answer. Type an expression using t as the variable.) OC. There is no solution.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....
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Transcribed Image Text:A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric acid, 75 pounds of nitrogen, and 20 pounds of potash; each barrel of mix B contains 30 pounds of phosphoric acid, 100 pounds of nitrogen, and 30
pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 30 pounds of potash; and each barrel of mix D contains 60 pounds of phosphoric acid, 25 pounds of nitrogen, and 50 pounds of potash.
Soil tests indicate that a particular field needs 840 pounds of phosphoric acid, 825 pounds of nitrogen, and 740 pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the
field?
Let x₁ be the number of barrels of Mix A, x2 be the number of barrels of Mix B, x3 be the number of barrels of Mix C, and x4 be the number of barrels of Mix D. Select the correct choice below and, if necessary, fill in the answer boxes to
complete your choice.
A. The unique solution is
=
=
=
=
X₁
X2
and X4
X3
(Simplify your answer.)
B. There are multiple combinations of how the barrels should be filled. The combinations are obtained from the equations X₁
₁ X₂ = ₁ X3 =
and x4 = t for
sts.
(Simplify your answer. Type an expression using t as the variable.)
OC. There is no solution.
"
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