https://file.aiquickdraw.com/mathbot/file/1726618297732ssntd8t2.jpg

The graph above shows the feasible region for the number of bags of Type A feed (\(x\)) and Type B feed (\(y\)) that the farmer can purchase. The shaded region represents the combinations of \(x\) and \(y\) that satisfy the following constraints:

1. **Oats constraint**: \(5x + 7y \geq 175\) (blue line).
2. **Corn constraint**: \(8x + 3y \geq 120\) (green line).
3. **Stock limits**: \(x \leq 30\) (red dashed line) and \(y \leq 25\) (orange dashed line).
4. **Non-negative values**: \(x \geq 0\) and \(y \geq 0\).

The shaded gray area shows the region where all these inequalities hold, indicating the valid choices for the number of Type A and Type B bags the farmer can buy.

Would you like a more detailed explanation of any of these constraints or how the graph was generated?

Here are some related questions to deepen your understanding:
1. How do you determine where the two lines intersect?
2. What does the region outside the shaded area represent?
3. How can you modify the constraints if the stock limit increases for either feed type?
4. Can the system of inequalities have no solution, and under what conditions?
5. How do you solve this system algebraically without graphing?

**Tip**: When solving inequalities graphically, always label and interpret the shaded region carefully to understand what real-world decisions it represents.

A store has two types of animal feed available. Type A contains 5 pounds of oats and 8 pounds of corn per bag. Type B contains 7 pounds of oats and 3 pounds of corn per bag. A farmer buys both types and combines them so that the resulting mixture has at least 175 pounds of oats and at least 120 pounds of corn. The store only has 30 bags of Type A feed and 25 bags of Type B feed in stock. Let x be the number of type A bags purchased. Let y be the number of type B bags purchased. Shade the region corresponding to all values of x and y that satisfy these requirements.

This problem involves solving a system of linear inequalities to determine the optimal combination of Type A and Type B feed bags, while satisfying constraints related to oats and corn quantities. Learn how to graph the solution and identify the feasible region.

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