Question

Write the solution of the following LPP \[ \text{Maximize } Z = x + y \] Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \] Which point the value of \( Z \) is maximum?

• A. \( (0, 4) \)
• B. \( (4, 0) \)
• C. \( (6, 0) \)
• D. \( (0, 6) \)

Hint:

Maximize or minimize the objective function by evaluating it at the vertices of the feasible region.

Answer 1

The Correct Option is D

The constraint \( 3x + 4y \leq 12 \) represents a line with the x-intercept \( x = 4 \) and the y-intercept \( y = 3 \). By evaluating the value of \( Z = x + y \) at each of the vertices of the feasible region, we find that the maximum value occurs at \( (0, 6) \) where \( Z = 6 \). Thus, the correct answer is \( (0, 6) \).