A fruit grower can use two types of fertilizer in her orange grove, brand A or brand B. The amounts (in pounds) of nitrogen, phosphoric acid, and chloride in a bag of each brand are given in the table. Tests indicate that the grove needs at least 1750 pounds of phosphoric acid and at most 350 pounds of chloride. Answer parts (A) and (B) below. Nitrogen Phosphoric Acid Chloride (A) If the grower wants to maximize the amount of nitrogen added to the grove, how many bags of each mix should be used? How much nitrogen will be added? The grower should add 0 bags of brand A and 350 bags of brand B to maximize the amount of nitrogen added. The maximum amount of nitrogen that will be added is 1750 pounds. (B) If the grower wants to minimize the amount of nitrogen added to the grove, how many bags of each mix should be used? How much nitrogen will be added? The grower should add bags of brand A and bags of brand B to minimize the amount of nitrogen added. Pounds per Bag Brand A 2 7 2 Brand B 5 7 1

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MINIMIZE the amount and what is the minimum amount of pounds?

## Fertilizer Optimization for Orange Groves

A fruit grower can use two types of fertilizer in her orange grove, brand A or brand B. The amounts (in pounds) of nitrogen, phosphoric acid, and chloride in a bag of each brand are given in the table below. Tests indicate that the grove requires at least 1750 pounds of phosphoric acid and at most 350 pounds of chloride. 

### Fertilizer Composition
| Pounds per Bag        | Brand A | Brand B |
|-----------------------|---------|---------|
| **Nitrogen**          | 2       | 5       |
| **Phosphoric Acid**   | 7       | 7       |
| **Chloride**          | 2       | 1       |

### Questions and Answers

#### (A) Maximizing Nitrogen Addition

- **Objective**: Maximize the amount of nitrogen added to the grove.
  
- **Solution**: 
  - The grower should use **0 bags of brand A** and **350 bags of brand B**.
  - This will add a **maximum of 1750 pounds** of nitrogen.

#### (B) Minimizing Nitrogen Addition

- **Objective**: Minimize the amount of nitrogen added to the grove.
  
- **Solution**: 
  - The grower should add a specific number of bags of brand A and brand B. (Exact numbers have not been provided in the document as the spaces are left blank.)

This analysis provides a detailed guide for managing fertilizer use by understanding the contents and requirements of the fertilizers applied to the grove.
Transcribed Image Text:## Fertilizer Optimization for Orange Groves A fruit grower can use two types of fertilizer in her orange grove, brand A or brand B. The amounts (in pounds) of nitrogen, phosphoric acid, and chloride in a bag of each brand are given in the table below. Tests indicate that the grove requires at least 1750 pounds of phosphoric acid and at most 350 pounds of chloride. ### Fertilizer Composition | Pounds per Bag | Brand A | Brand B | |-----------------------|---------|---------| | **Nitrogen** | 2 | 5 | | **Phosphoric Acid** | 7 | 7 | | **Chloride** | 2 | 1 | ### Questions and Answers #### (A) Maximizing Nitrogen Addition - **Objective**: Maximize the amount of nitrogen added to the grove. - **Solution**: - The grower should use **0 bags of brand A** and **350 bags of brand B**. - This will add a **maximum of 1750 pounds** of nitrogen. #### (B) Minimizing Nitrogen Addition - **Objective**: Minimize the amount of nitrogen added to the grove. - **Solution**: - The grower should add a specific number of bags of brand A and brand B. (Exact numbers have not been provided in the document as the spaces are left blank.) This analysis provides a detailed guide for managing fertilizer use by understanding the contents and requirements of the fertilizers applied to the grove.
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