### Problem Statement: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 400 pounds of phosphoric acid, 990 pounds of nitrogen, and 220 pounds of potash. If mix A costs $20 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?### Requirements and Costs:- **Mix A:** - 20 pounds of phosphoric acid - 30 pounds of nitrogen - 5 pounds of potash - Cost: $20 per cubic yard- **Mix B:** - 10 pounds of phosphoric acid - 30 pounds of nitrogen - 10 pounds of potash - Cost: $35 per cubic yard### Minimum Monthly Requirements:- 400 pounds of phosphoric acid- 990 pounds of nitrogen- 220 pounds of potash### Objective:Find the number of cubic yards of mix A and mix B the farmer should blend to meet the minimum monthly requirements at a minimum cost and determine that cost.**If mix A costs $20 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend:**- __ cubic yards of mix A and - __ cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.The cost is $ __ .

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 400 pounds of phosphoric acid, 990 pounds of nitrogen, and 220 pounds of potash. If mix A costs $20 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 $20 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend meet the minimum monthly requirements at a minimum cost. ] va² of mix A andya of mix B to The cost is S

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 400 pounds of phosphoric acid, 990 pounds of nitrogen, and 220 pounds of potash. If mix A costs $20 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 $20 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend meet the minimum monthly requirements at a minimum cost. ] va² of mix A andya of mix B to The cost is S

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

### Problem Statement:

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 400 pounds of phosphoric acid, 990 pounds of nitrogen, and 220 pounds of potash. If mix A costs $20 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?

### Requirements and Costs:
- **Mix A:**
- 20 pounds of phosphoric acid
- 30 pounds of nitrogen
- 5 pounds of potash
- Cost: $20 per cubic yard

- **Mix B:**
- 10 pounds of phosphoric acid
- 30 pounds of nitrogen
- 10 pounds of potash
- Cost: $35 per cubic yard

### Minimum Monthly Requirements:
- 400 pounds of phosphoric acid
- 990 pounds of nitrogen
- 220 pounds of potash

### Objective:
Find the number of cubic yards of mix A and mix B the farmer should blend to meet the minimum monthly requirements at a minimum cost and determine that cost.

**If mix A costs $20 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend:**
- __ cubic yards of mix A and
- __ cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.

The cost is $ __ .

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