The corner points of a feasible region of a LPP are (0, 0), (0, 1) and (1, 0). If the objective function is Z = 7x + y, then `Z_("max") - Z_("min")` =

Options

A. 0
B. 1
C. 7
D. 6

Answer

To solve the problem, we need to evaluate the objective function \( Z = 7x + y \) at the corner points of the feasible region, which are given as (0, 0), (0, 1), and (1, 0). We will then determine the maximum and minimum values of \( Z \) and calculate \( Z_{\text{max}} - Z_{\text{min}} \).

### Step-by-Step Solution:

1. **Identify the corner points**:
The corner points of the feasible region are:
- Point A: \( (0, 0) \)
- Point B: \( (0, 1) \)
- Point C: \( (1, 0) \)

2. **Calculate \( Z \) at each corner point**:
- For Point A \( (0, 0) \):
\[ Z_A = 7(0) + 0 = 0 \]
- For Point B \( (0, 1) \):
\[ Z_B = 7(0) + 1 = 1 \]
- For Point C \( (1, 0) \):
\[ Z_C = 7(1) + 0 = 7 \]

3. **Determine the maximum and minimum values of \( Z \)**:
- The maximum value of \( Z \) is:
\[ Z_{\text{max}} = \max(Z_A, Z_B, Z_C) = \max(0, 1, 7) = 7 \]
- The minimum value of \( Z \) is:
\[ Z_{\text{min}} = \min(Z_A, Z_B, Z_C) = \min(0, 1, 7) = 0 \]

4. **Calculate \( Z_{\text{max}} - Z_{\text{min}} \)**:
\[ Z_{\text{max}} - Z_{\text{min}} = 7 - 0 = 7 \]

### Final Answer:
\[ Z_{\text{max}} - Z_{\text{min}} = 7 \]