An Airline operates flight between 2 major cities and has two classes of tickets, Economy and Business.

• Each Economy seat costs Rs. 5,000 and has 150 available seats.
• Each Business costs Rs. 12,000 and has 50 available seats.
• Total passenger capacity is 180.
• Airline must cover at least Rs. 10,00,000 in operation cost.

Find the optimal $(x,y)$ for the LPP.

$(166,14)$

The correct answer is Option (4) → $(166,14)$

Find the intersection between,

$x+y=180$   ...(1)

$5x+12y=1000$   ...(2)

$⇒5x+12(180-x)=1000$

$⇒-7x=-1160$

$⇒x=\frac{1160}{7}≃166$

$∴y=14$

and, $Z_{max}=Z(166,14)$