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The images provide details about an agricultural production planning problem for Margaret Black, who manages five parcels of land and grows wheat, alfalfa, and barley. The goal is to formulate a production plan, determine the most profitable crop mix, and assess the impact of an additional water allotment.

### Given Data:

#### Parcel Information:
| Parcel     | Area (Acres) | Water Irrigation Limit (Acre-Feet) |
|------------|--------------|-----------------------------------|
| Southeast  | 2,000        | 3,200                             |
| North      | 2,300        | 3,400                             |
| Northwest  | 600          | 800                               |
| West       | 1,100        | 500                               |
| Southwest  | 500          | 600                               |

Total land area: 6,500 acres  
Total water available: 7,400 acre-feet

#### Crop Information:
| Crop     | Maximum Sales        | Water Needed Per Acre (Acre-Feet) | Profit |
|----------|----------------------|-----------------------------------|--------|
| Wheat    | 110,000 bushels       | 1.6                               | $2/bushel |
| Alfalfa  | 1,800 tons            | 2.9                               | $40/ton |
| Barley   | 2,200 tons            | 3.5                               | $50/ton |

### Additional Data:
- Wheat yield: 50 bushels/acre
- Alfalfa yield: 1.5 tons/acre
- Barley yield: 2.2 tons/acre

### Objectives:
1. **(a) Formulate Margaret's production plan**:
   - You need to allocate land and water optimally for each crop while respecting the area and water limits of each parcel.

2. **(b) What should the crop plan be, and what profit will it yield?**:
   - This requires a mathematical optimization of land and water usage across the different crops to maximize profit.

3. **(c) Impact of an additional 600 acre-feet of water**:
   - Assess the profitability of paying $6,000 for extra water, and how it affects the crop allocation.

### Step-by-Step Approach:
To solve this problem, we can use a linear programming approach. The steps include:
1. **Decision Variables**: Define the area of each crop in each parcel.
2. **Constraints**:
   - Total area for each parcel.
   - Water limits for each parcel.
   - Total water allotment (7,400 acre-feet, potentially 8,000 with extra purchase).
   - Maximum sales limits.
3. **Objective Function**: Maximize the total profit from wheat, alfalfa, and barley.

Would you like me to formulate the equations and constraints, or proceed directly to solving the optimization problem? 

### Related Questions:
1. How is the profit calculated for each crop in terms of yield and price?
2. What are the limitations in planting specific crops on certain parcels?
3. How would the crop yield affect water distribution?
4. Can we explore alternative uses for the extra water if it is purchased?
5. How would the total profit change if water availability is increased?

### Tip:
Using linear programming tools or solver software can significantly simplify multi-variable optimization problems like this one.

Margaret Black's family owns five parcels of farmland and is involved in growing wheat, alfalfa, and barley. Given the water and land constraints, as well as crop yields and profitability, formulate a production plan, determine the optimal crop plan, and assess whether to buy additional water for $6,000.

Solve the agricultural production planning problem for Margaret Black's farm, involving the optimization of wheat, alfalfa, and barley crops under water and land constraints. Learn to use linear programming to maximize profit while considering yield, water limits, and additional water allotment costs.

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