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?
Answer & explanation
Correct answer: option 1
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 $a+b=12$,
$a+9=12$
$a=3$
$a=3,b=9$