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:

50

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 $Z_{max}=Z_{(8, 2)}=8a+2b=50$