The corner points of the feasible region of an LPP are (0,0),(0,8),(2,7),(5,4) and (6,0). The maximum value of the objective function Z = 3x + 2y is:

Options

A. 20
B. 23
C. 27
D. 18

Answer

To find the maximum value of the objective function \( Z = 3x + 2y \) at the corner points of the feasible region, we will evaluate \( Z \) at each of the given corner points: \( (0,0) \), \( (0,8) \), \( (2,7) \), \( (5,4) \), and \( (6,0) \).

### Step-by-Step Solution:

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

2. **Evaluate \( Z \) at point \( B(0,8) \)**:
\[ Z = 3(0) + 2(8) = 0 + 16 = 16 \]

3. **Evaluate \( Z \) at point \( C(2,7) \)**:
\[ Z = 3(2) + 2(7) = 6 + 14 = 20 \]

4. **Evaluate \( Z \) at point \( D(5,4) \)**:
\[ Z = 3(5) + 2(4) = 15 + 8 = 23 \]

5. **Evaluate \( Z \) at point \( E(6,0) \)**:
\[ Z = 3(6) + 2(0) = 18 + 0 = 18 \]

6. **Compare all the values of \( Z \)**:
- \( Z(A) = 0 \)
- \( Z(B) = 16 \)
- \( Z(C) = 20 \)
- \( Z(D) = 23 \)
- \( Z(E) = 18 \)

7. **Determine the maximum value**:
The maximum value of \( Z \) occurs at point \( D(5,4) \) where \( Z = 23 \).

### Conclusion:
The maximum value of the objective function \( Z = 3x + 2y \) is **23**.