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 500 pounds of phosphoric acid, 990 pounds of nitrogen, and 200 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $40 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 500 pounds of phosphoric acid, 990 pounds of nitrogen, and 200 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $40 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?
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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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 500 pounds of phosphoric acid, 990 pounds of nitrogen, and 200 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $40 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?
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 500 pounds of phosphoric acid, 990 pounds of nitrogen, and 200 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $40 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 S25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blendOyd of mix A and yd of mix B to meet the minimum monthly requirements at a minimum cost.
The cost is S.
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