If a corner points of the feasible solutions are (0,10)(2,2)(4,0) (3,2) then the point of minimum Z=3x +2y is

Options

A. (2,2)
B. (0,10)
C. (4,0)
D. (3,2)

Answer

To find the point of minimum \( Z = 3x + 2y \) given the corner points of the feasible solutions (0,10), (2,2), (4,0), and (3,2), we will evaluate the objective function \( Z \) at each of these points.

### Step-by-Step Solution:

1. **Evaluate \( Z \) at point (0, 10)**:
\[ Z = 3(0) + 2(10) = 0 + 20 = 20 \]

2. **Evaluate \( Z \) at point (2, 2)**:
\[ Z = 3(2) + 2(2) = 6 + 4 = 10 \]

3. **Evaluate \( Z \) at point (4, 0)**:
\[ Z = 3(4) + 2(0) = 12 + 0 = 12 \]

4. **Evaluate \( Z \) at point (3, 2)**:
\[ Z = 3(3) + 2(2) = 9 + 4 = 13 \]

5. **Compare the values of \( Z \)**:
- At (0, 10), \( Z = 20 \)
- At (2, 2), \( Z = 10 \)
- At (4, 0), \( Z = 12 \)
- At (3, 2), \( Z = 13 \)

6. **Identify the minimum value**:
The minimum value of \( Z \) occurs at the point (2, 2) where \( Z = 10 \).

### Conclusion:
The point of minimum \( Z = 3x + 2y \) is at \( (2, 2) \).

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