A farmer can buy four types of plant food. Each barrel of mix A contains 25 pounds of phosphoric acid, 50 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 35 pounds of phosphoric acid, 75 pounds of nitrogen, and 20 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 20 pounds of potash; each barrel of mix D contains 80 pounds of phosphoric acid, 50 pounds of nitrogen, and 70 pounds of potash. Soil tests indicate that a particular field needs 1,095 pounds of phosphoric acid, 975 pounds of nitrogen, and 880 pounds of potash. There are multiple solutions to the number of barrels of each type of food that could be mixed together to supply the necessary nutrients for the field. The solutions can be expressed as (10 -t) barrels of mix A, (t- 5) barrels of mix B, (34 - 3t) barrels of mix C, and t barrels of mix D, where t is an integer satisfying 5sts 10. The costs of the four mixes are Mix A, $40, Mix B, $74, Mix C, $55, Mix D, $59. Which of the solutions to the problem of supplying the correct nutrients would minimize the cost of the plant food? Let the variables x, represent the number of barrels of mixture A, x, represent the number of barrels of mixture B, x, represent the number of barrels of mixture C and x represent the number of barrels of mixture D. Write the equation that can be used to find the cost C in terms of the variables x, through x. (Do not include the $ symbol in your answer.)
A farmer can buy four types of plant food. Each barrel of mix A contains 25 pounds of phosphoric acid, 50 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 35 pounds of phosphoric acid, 75 pounds of nitrogen, and 20 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 20 pounds of potash; each barrel of mix D contains 80 pounds of phosphoric acid, 50 pounds of nitrogen, and 70 pounds of potash. Soil tests indicate that a particular field needs 1,095 pounds of phosphoric acid, 975 pounds of nitrogen, and 880 pounds of potash. There are multiple solutions to the number of barrels of each type of food that could be mixed together to supply the necessary nutrients for the field. The solutions can be expressed as (10 -t) barrels of mix A, (t- 5) barrels of mix B, (34 - 3t) barrels of mix C, and t barrels of mix D, where t is an integer satisfying 5sts 10. The costs of the four mixes are Mix A, $40, Mix B, $74, Mix C, $55, Mix D, $59. Which of the solutions to the problem of supplying the correct nutrients would minimize the cost of the plant food? Let the variables x, represent the number of barrels of mixture A, x, represent the number of barrels of mixture B, x, represent the number of barrels of mixture C and x represent the number of barrels of mixture D. Write the equation that can be used to find the cost C in terms of the variables x, through x. (Do not include the $ symbol in your answer.)
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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Transcribed Image Text:A farmer can buy four types of plant food. Each barrel of mix A contains 25 pounds of phosphoric acid, 50 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 35 pounds of phosphoric acid, 75 pounds of nitrogen, and 20
pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 20 pounds of potash; each barrel of mix D contains 80 pounds of phosphoric acid, 50 pounds of nitrogen, and 70 pounds of potash. Soil
tests indicate that a particular field needs 1,095 pounds of phosphoric acid, 975 pounds of nitrogen, and 880 pounds of potash. There are multiple solutions to the number of barrels of each type of food that could be mixed together to supply the
necessary nutrients for the field. The solutions can be expressed as (10 – t) barrels of mix A, (t - 5) barrels of mix B, (34 - 3t) barrels of mix C, and t barrels of mix D, where t is an integer satisfying 5sts 10.
The costs of the four mixes are Mix A, $40, Mix B, $74, Mix C, $55, Mix D, $59. Which of the solutions to the problem of supplying the correct nutrients would minimize the cost of the plant food?
Let the variables x, represent the number of barrels of mixture A, x, represent the number of barrels of mixture B, xX3 represent the number of barrels of mixture C and x4 represent the number of barrels of mixture D. Write the equation that can
be used to find the cost C in terms of the variables x, through x4.
(Do not include the $ symbol in your answer.)
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