The objective function of an LPP is $Z = ax + by$. If the maximum value of the objective function is 180, which occurs at two points (15, 15) and (0, 20), then which one of the following is true?

$a=3, b = 9$

The correct answer is Option (1) → $a=3, b = 9$

$Z=ax+by$

Given maximum value $Z=180$ occurs at $(15,15)$ and $(0,20)$.

At $(15,15)$,

$15a+15b=180$

$a+b=12$

At $(0,20)$,

$20b=180$

$b=9$

Substitute $b=9$ in $a+b=12$,

$a+9=12$

$a=3$

$a=3,b=9$