A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen, and 10 pounds of potash. The minimum monthly requirements are 440 pounds of phosphoric acid, 960 pounds of nitrogen, and 200 pounds of potash. If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost? If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend yd of mix A and yd3 of mix B to meet the minimum monthly requirements at a minimum cost.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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A farmer can buy two types of plant​ food, mix A and mix B. Each cubic yard of mix A contains

20

pounds of phosphoric​ acid,

30

pounds of​ nitrogen, and

5

pounds of potash. Each cubic yard of mix B contains

10

pounds of phosphoric​ acid,

30

pounds of​ nitrogen, and

10

pounds of potash. The minimum monthly requirements are

440

pounds of phosphoric​ acid,

960

pounds of​ nitrogen, and

200

pounds of potash. If mix A costs

​$30

per cubic yard and mix B costs

​$35

per cubic​ yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum​ cost? What is this​ cost?

A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen,
and 10 pounds of potash. The minimum monthly requirements are 440 pounds of phosphoric acid, 960 pounds of nitrogen, and 200 pounds of potash. If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix
should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost?
If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend yd3 of mix A and yd3 of mix B to meet the minimum monthly requirements at a minimum cost.
Transcribed Image Text:A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen, and 10 pounds of potash. The minimum monthly requirements are 440 pounds of phosphoric acid, 960 pounds of nitrogen, and 200 pounds of potash. If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost? If mix A costs $30 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend yd3 of mix A and yd3 of mix B to meet the minimum monthly requirements at a minimum cost.
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