The maximum value of $Z=5x+3y $ subject to the constraints $2x+4y≤16, 3x+y ≤9, x, y ≥0$ is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 19
$3x+y=9$ ...(1)
$2x+4y=16$ ...(2)
$\text{4×Eq. (1)-Eq. (2)}$, we get
$10x=20$
$x=2⇒y=3$
Objective, $Z=5x+3y$
$Z(0,0)=0$
$Z(0,4)=12$
$Z(3,0)=15$
$Z(2,3)=5×2+3×3=19$ → maximum value