An objective function $Z=a x+b y$ is maximum at points (8, 2) and (4, 6). If a ≥ 0 and b ≥ 0 and ab = 25, then the maximum value of the function is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - 50
$Z=a x+b y$
max at (8, 2) and (4, 6)
$Z_{(8, 2)}=Z_{(4, 6)}$
$8a+2b=4a+6b$
$4a=4b⇒a=b$
given $ab=25$
$a^2=25⇒a=5=b$
as $a,b≥0$
so $Z_{max}=Z_{(8, 2)}=8a+2b=50$