Maximize Z=3x+4y, subject to the constraints: x +y≤1,x≥0,y≥0.

The correct answer is Option (4) → 4

Draw the constraint $x + y = 1$

Find intercepts:

• When $x=0, y=1$
• When $y=0, x=1$

So the line joins points (0,1) and (1,0).

The shaded region shown in the figure as OAB is bounded and the coordinates of corner points O, A and B are (0, 0), (1, 0) and (0, 1), respectively.

Corner points	Corresponding value of $Z=3x+4y$
(0,0)	0
(1,0)	3
(0,1)	4 → Maximum

Hence, the maximum value of Z is 4 at (0, 1).