Q.The maximum value of the objective function $Z = 3x + 5y$ subject to the constraints $2x + 5y \le 10$, $x \ge 0$, $y \ge 0$ is :

The corner points give $Z=0,15,10$; the maximum is $15$ at $(5,0)$, so the answer is option (d).

We maximise $Z = 3x + 5y$ subject to

$2x + 5y \le 10,\quad x \ge 0,\quad y \ge 0.$

Find the corner points of the feasible region. The boundary line $2x + 5y = 10$ meets the axes at:

• $x$-axis $(y=0)$: $2x = 10 \Rightarrow x = 5$, point $(5, 0)$.
• $y$-axis $(x=0)$: $5y = 10 \Rightarrow y = 2$, point $(0, 2)$. …