The maximum value of z = 4x + 3y subject to constraint x + y ≤ 6, x, y ≥ 0 is :

24

z = 4x + 3y → function

constrains x + y ≤ 6

x, y ≥ 0  (in first quadrant)

plotting first for x + y = 6

Now checking for (0, 0) point for inequality x + y ≤ 6

0 ≤ 6

⇒ Solution lies to side of equation x + y =6

containing (0, 0)

Corner points obtained

(0, 0)

(0, 6)

(6, 0)

function z = 4x + 3y

z(x, y) = 4x + 3y

So z(0, 0) = 0 + 0 = 0

z(0, 6) = 18

z(6, 0) = 24

Max value is at point (6, 0)

which is 24