If the objective function for a L.P.P. is `Z=5x+7y` and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

Options

A. A) (0, 0)
B. B) (7, 0)
C. C) (3, 4)
D. D) (0, 2)

Answer

To solve the problem, we need to evaluate the objective function \( Z = 5x + 7y \) at each of the given corner points of the feasible region. The corner points provided are (0, 0), (7, 0), (3, 4), and (0, 2). We will calculate the value of \( Z \) at each point and determine which one gives the maximum value.

### Step-by-step Solution:

1. **Evaluate \( Z \) at the point (0, 0)**:
\[ Z = 5(0) + 7(0) = 0 + 0 = 0 \]

2. **Evaluate \( Z \) at the point (7, 0)**:
\[ Z = 5(7) + 7(0) = 35 + 0 = 35 \]

3. **Evaluate \( Z \) at the point (3, 4)**:
\[ Z = 5(3) + 7(4) = 15 + 28 = 43 \]

4. **Evaluate \( Z \) at the point (0, 2)**:
\[ Z = 5(0) + 7(2) = 0 + 14 = 14 \]

5. **Compare the values of \( Z \)**:
- At (0, 0), \( Z = 0 \)
- At (7, 0), \( Z = 35 \)
- At (3, 4), \( Z = 43 \)
- At (0, 2), \( Z = 14 \)

6. **Determine the maximum value of \( Z \)**:
The maximum value of \( Z \) occurs at the point (3, 4) where \( Z = 43 \).

### Conclusion:
The maximum value of \( Z \) occurs at the point (3, 4), and the maximum value is \( 43 \).