A charter airline finds that on its Saturday flights from Philadelphia to London all 180 seats will be sold if the ticket price is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one. (a) Find a formula for the number of seats sold S if the ticket price is P dollars.

Step-by-step explanation:

Given that:

Number of seats sold is 180 with ticket price $200.

Number of seats decreases by one when the ticket price is increased by $3.

To find:

The formula for the number of seats sold (S) when the ticket price is P dollars.

Solution:

It is linear dependency of number of seats sold, S on ticket price, P.

It can be written as:

Where is the constant of proportionality and

is a constant.

Now, putting the given values:

...... (2)

Subtracting (1) from (2):

Putting the value in (1):

Therefore the equation becomes:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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