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Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points x + 4y <= 24; 5x + y <= 25; z >= 0; y >= 0 10+ 8 3 2 2 N 35 6 7 8 9

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Answer to a math question Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points x + 4y <= 24; 5x + y <= 25; z >= 0; y >= 0 10+ 8 3 2 2 N 35 6 7 8 9

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Tiffany
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102 Answers
1. **Graph the first inequality**: x + 4y \leq 24
- Find the intercepts:
- When x = 0 : 4y \leq 24 \implies y \leq 6
- When y = 0 : x \leq 24

2. **Graph the second inequality**: 5x + y \leq 25
- Find the intercepts:
- When x = 0 : y \leq 25
- When y = 0 : 5x \leq 25 \implies x \leq 5

3. **Include non-negativity constraints**: x \geq 0 and y \geq 0

4. **Find intersection points of the boundary lines**:
- Intersection of x + 4y = 24 and 5x + y = 25 :
- Solve:
\begin{cases} x + 4y = 24 \\ 5x + y = 25 \\ \end{cases}
- Multiply the second equation by 4:
5x + y = 25 \implies 20x + 4y = 100
- Subtract the first equation from this result:
20x + 4y - x - 4y = 100 - 24 \implies 19x = 76 \implies x = 4
- Substitute x = 4 back into 5x + y = 25 :
5(4) + y = 25 \implies y = 5

5. **Determine the vertices**:
- Intercepts at:
- (0, 0)
- (0, 6)
- (4, 5)
- (5, 0)

6. **Plot these points and connect them to form the polygon representing the feasible region**.

Answer:
(0,0), (0,6), (4,5), (5,0)

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