Consider $\"\"$ is the number of first class seats and $\"\"$ is the number of coach seats.

The revenue from $\"\"$ first class seats and $\"\"$ coach seats is $\"\"$ where $\"\"$ .

Henc e $\"\"$ is the objective function to be maximized.

The constraints are :

Restriction on first lass seats is $\"\"$ .

Restriction on coach seats is $\"\"$ .

(a)

Find the each number of seats to maximize the revenue.

The ratio of first class to coach seats shoud never exceed $\"\"$ .

Hence $\"\"$ .

The constraints are $\"\"$ , $\"\"$ and $\"\"$ .

Graph :

$\"\"$

Observe the graph the corner points are $\"\"$ , $\"\"$ and $\"\"$ .

The function is $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Since $\"\"$ , $\"\"$ .

Hence $\"\"$ .

Since $\"\"$ , $\"\"$ .

Hence $\"\"$ .

Therefore, the maximum revenue occurs when the aircraft is configured with $\"\"$ first class seats and $\"\"$ coach seats.

(b)

Find the each number of seats to maximize the revenue.

The ratio of first class to coach seats shoud never exceed $\"\"$ .

Hence $\"\"$ .

The constraints are $\"\"$ , $\"\"$ and $\"\"$ .

Graph :

$\"\"$

Observe the graph the corner points are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

The function is $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Since $\"\"$ and $\"\"$ , $\"\"$ .

Hence the maximum value of $\"\"$ occurs at $\"\"$ .

Therefore, the maximum revenue occurs when the aircraft is configured with $\"\"$ first class seats and $\"\"$ coach seats.

(a) The maximum revenue occurs when the aircraft is configured with $\"\"$ first class seats and $\"\"$ coach seats.

(b) The maximum revenue occurs when the aircraft is configured with $\"\"$ first class seats and $\"\"$ coach seats.