What is the Optimal Price for a Magazine with 140 Thousand Monthly Circulation?

[cybershell]

well I'm having an off day today an I wasn't able to solve some problem that was given to me in a formal manner, and it's kinda bugging me...here goes

A magazine has a circulation of 140 thousand per month when they charge $2.50 for a magazine. For each $.10 increase in price, 5 thousand sales are lost. how much should be charged per magazine to maximize revenue?

 

[Alfredwolf]

this problem is a tad easy(I hope), from reading it you can make a parabolic model
such that

y=[2.5+(1/10)x]*[140,000-5000x]
from here by multiplying out the binomials we get

y=-500x^2+1500x+350,000

remember that when f'(x)=0 the tangent to the curve will hit the extrema (minimum/maximum)

and we get y'=(-1000x)+1500
setting the derivative to 0 gives us
1.5 so the amount that will maximize this is x=1.50

(hope I'm right and that that helped you a bit, by the way I'm a 9th grader in algebra 2 and I've seen a problem similar to this ,are you sure this isn't a homework problem?)

 

[Gib Z]

Yes It seems to me like it was a homework question, and you state that you suspect that, and since I'm sure you read the terms and conditions before you made your account, rather than just press next, you would know not to give out full solutions to homework problems. Sorry, I know its a harsh way to start here at PF, but those are the rules.

by the way I'm a 9th grader in algebra 2

How was that relevant in any way ..

 

[HallsofIvy]

Well, it's just a 'tad' harsh!