Question

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert...?
...it will sell 50 – x box seats. The function S = 50x – x2 gives the estimated income from the sale of the box seats.
(this is the rest of the problem)

i cant figure this out. if you can please explain it it will be a big help please and thank you:)

Answer 1

You want the no. of tickets for maximising profit?

Answer 2

well i get 25 but it isnt right

Answer 3

Correct. S = x * (50 - x) = 50x - x^2

You may want to know what the maximum income S(x) is:

dS/dx = 50 - 2x = 0; x = 25

S(25) = 25 * 25 = 625

The maximum income is $625. The ticket price for that is $25.

Answer 4

Umm, you figured out the problem totally right.
Do check again if you copied the question correctly. Is there a chance of a printing or typing error where the question was stated?

Answer 5

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x box seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income

Answer 6

Well, you have solved it exactly as you should have done, and your answers are correct as well. (I am getting the same answers as well)

What's the correct answer according to the book?

Answer 7

i dont know ... i just did a test and 25 was incorrect :(

Answer 8

Don't worry, consult your teacher regarding this, s/he might have made mistake in the correction. Or check with your classmates.

(just confirming, "charges x dollars for box seats" definitely means the price 'per seat' right? Couldn't mean anything else, could it?)

Answer 9

no not really... ill ask my teacher n see thx :P

Answer 10

No problem