A farmer can use three types of plant food: mix A, mix B, and mix C. The amounts (in pounds) of nitrogen, phosphoric acid, and potash in a cubic yard of each mix are given in the table. Tests performed on the soil indicate that the field needs at least 1000 pounds of potash. The tests also indicate that no more than 800 pounds of phosphoric acid should be added to the field. The farmer plans to plant a crop that requires a great deal of nitrogen. How many cubic yards of each mix should be added to the field in order to satisfy the potash and phosphoric acid requirements and maximize the amount of nitrogen? What is the maximum amount of nitrogen? Pounds per Cubic Yard A B Nitrogen Phosphoric 15 20 10 8 16 acid Potash 16 16 Construct a mathematical model in the form of a linear programming problem. Use x, to represent the cubic yards of mix A, x, to represent the cubic yards of mix B, and x3 to represent the cubic yards of mix C. Maximize P = subject to V 1000 V 800 X1, X2, X3 8 o co

A farmer can use three types of plant food: mix A, mix B, and mix C. The amounts (in pounds) of nitrogen, phosphoric acid, and potash in a cubic yard of each mix are given in the table. Tests performed on the soil indicate that the field needs at least 1000 pounds of potash. The tests also indicate that no more than 800 pounds of phosphoric acid should be added to the field. The farmer plans to plant a crop that requires a great deal of nitrogen. How many cubic yards of each mix should be added to the field in order to satisfy the potash and phosphoric acid requirements and maximize the amount of nitrogen? What is the maximum amount of nitrogen? Pounds per Cubic Yard A B Nitrogen Phosphoric 15 20 10 8 16 acid Potash 16 16 Construct a mathematical model in the form of a linear programming problem. Use x, to represent the cubic yards of mix A, x, to represent the cubic yards of mix B, and x3 to represent the cubic yards of mix C. Maximize P = subject to V 1000 V 800 X1, X2, X3 8 o co

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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Question

A farmer can use three types of plant food: mix A, mix B, and mix C. The amounts (in pounds) of nitrogen, phosphoric acid, and potash in a
cubic yard of each mix are given in the table. Tests performed on the soil indicate that the field needs at least 1000 pounds of potash. The tests
also indicate that no more than 800 pounds of phosphoric acid should be added to the field. The farmer plans to plant a crop that requires a
great deal of nitrogen. How many cubic yards of each mix should be added to the field in order to satisfy the potash and phosphoric acid
requirements and maximize the amount of nitrogen? What is the maximum amount of nitrogen?
Pounds per Cubic Yard
A
B
Nitrogen
Phosphoric
15
20
10
8
16
acid
Potash
16
16
Construct a mathematical model in the form of a linear programming problem. Use x, to represent the cubic yards of mix A, x, to represent the cubic yards of mix B, and x3 to represent the cubic
yards of mix C.
Maximize
P =
subject to
V 1000
V 800
X1,
X2,
X3
8 o co

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