Question

A chartered plane has 200 seats and charges of 3000 are taken per seat with an additional charge of 150 for each subsequent cancellation. Find the total revenue function in terms of the number of cancellations before the departure of the plane. Also, find the number of cancellations for which total revenue is maximum.​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

The charter plane has 200 Seats.
The Cost per ticket is 3000. In such case, the Revenue generated is

R  = 200 * 3000 = 600,000.

Now, if there is subsequent cancellation then the Cost per tickets increase by 150 per ticket. So if x tickets are cancelled then the Cost per ticket for remaining tickets is 3000 - 150x. So revenue in such case is,

R = (3000 + 150$x$) * (200 - $x$)

R = 600000 + 27000x - 150$x^{2}$

So, dR / d$x$  = 27000 - 300$x$

now to have maximum revenue dR / d$x$ should be 0

Hence, 27000 - 300$x$ = 0

therefore, $x$  = 90.

Hence, at 90 cancellations the Revenue is maximum.