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.)
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....
Related questions
Question
I want correct handwritten solution only otherwise skip please
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.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
