• Sep 18th 2005, 11:07 PM
steve
A company sells 200 boat tickets for \$50 each. For every \$10 increase in the ticket price 5 fewer tickets will be sold.

Represent the number of tickets sold as a function of the selling price.

Represent the revenue as a function of the selling price.

Thanks to all who help.
• Sep 19th 2005, 06:38 AM
hemza
Hi,

Ok, so at first for price=\$50/ticket there will be 200 tickets sold and when the price goes \$60/ticket there will be 195 tickets sold.

So the number of tickets (n) depends on the price (p). And we have

p n
50 200
60 195
70 190
...

It is linear : if you draw the function you see it (see figure). So, you calculate the slope for two of the points. Here, I chose (50;200) which is \$50 -> 200 tickets and the point (70;190) which is \$70 -> 190 tickets. So slope = (200-190)/(50-70) = -10/20=-1/2 so our linear function (y=mx+b) is y =
-1/2 x +b. We replace by the coordinates of (50;200) and we get 200=-1/2*50+b so b=200+25=225. So y=-1/2 x +225. Since our variables are p (the independent one) which is x and n which is y. We get n=-1/2 p + 225 (number of tickets sold as a function of the selling price).

(This function is only defined for price p between \$50 and \$450 because it begins at \$50 and at \$450 dollars n=-1/2*450+225=0 so after, n will ne negative which is impossible.)

Now, the revenue R is what they get in cash so for every ticket they get the price of the ticket in cash so they get n*p (if there are 200 tickets at \$50 each they get 200*\$50=\$10000 in cash) so R=n*p (revenue as a function of the selling price).

So in general, Y as a function of X is Y=...x....... (Y=something expression containing x)
• Sep 19th 2005, 03:49 PM
steve
Wow thanks for the help. The imaged made it easier to understand. :D