The corner points of the feasible region determined by a system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). If the objective function is $Z=4x+3y$, then which one of the following is true?

$\text{Max. Z < 400}$

The correct answer is Option (2) → $\text{Max. Z < 400}$

Given objective function: $Z = 4x + 3y$

Corner points:

(0, 0), (0, 40), (20, 40), (60, 20), (60, 0)

Compute $Z$ at each corner point:

At (0, 0): $Z = 4(0) + 3(0) = 0$

At (0, 40): $Z = 4(0) + 3(40) = 120$

At (20, 40): $Z = 4(20) + 3(40) = 80 + 120 = 200$

At (60, 20): $Z = 4(60) + 3(20) = 240 + 60 = 300$

At (60, 0): $Z = 4(60) + 3(0) = 240$

Maximum value: $Z_{\max} = 300$ at $(60, 20)$

Minimum value: $Z_{\min} = 0$ at $(0, 0)$

Therefore, $Z_{\max} = 300$ at $(60, 20)$ and $Z_{\min} = 0$ at $(0, 0)$.