State True or False:
If the corner points of the feasible region are (0, 10),(2, 2) & (4, 0) then the minimum value of Z = 3x + 2y is at (4, 0)

Answer

To determine whether the statement is true or false, we need to evaluate the function \( Z = 3x + 2y \) at the given corner points of the feasible region: (0, 10), (2, 2), and (4, 0).

### Step-by-Step Solution:

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

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

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

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

5. **Identify the minimum value**:
The minimum value of \( Z \) among the calculated values is \( 10 \), which occurs at the point (2, 2).

6. **Conclusion**:
Since the minimum value of \( Z = 3x + 2y \) is at (2, 2) and not at (4, 0), the statement is **False**.