The maximum value of $Z=2x+3y$ subject to the constraints $x ≥0, y ≥ 0; x+y ≤10, 3x+4y ≤ 36 $ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 27
$x, y ≥ 0; x+y ≤10, 3x+4y ≤ 36$
| corner points | $Z=2x+3y$ |
| $A(0, 9)$ | $Z_A=27$ |
| $B(4,6)$ | $Z_B=26$ |
| $C(10,0)$ | $Z_C=20$ |
| $D(0,0)$ | $Z_D=0$ |
$Z_A=27$ → maximum value