Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is:
C(x) = 2950 + 6x + 0.1x2 (0 ≤ x ≤ 500).
Gymnast Clothing sells the cleats at $130 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?

I've worked this problem out so many times I'm almost sick of looking at it, and I still haven't come up with the correct answer.

Question

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is:
C(x) = 2950 + 6x + 0.1x2    (0 ≤ x ≤ 500). 
Gymnast Clothing sells the cleats at $130 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?

I've worked this problem out so many times I'm almost sick of looking at it, and I still haven't come up with the correct answer.

riley · Answer

This is what I keep coming up with:

Revenue: R(x) = 130x
Profit: P(x) = .2950+124x-0.1x^2
And for the pairs of shoes I'm getting 23.5. 

When I was working through the profit formula however, to find the break-even point I set the equation equal to 0, and then solved for x.  I ended up with a quadratic equation so I used the quadratic formula to solve that part.

I ended up getting:

= 23.5 or -1263.5;  And because of the domain being from 0 to 500 I assumed the answer had to be 23.5 . . . however this isn't correct and I can't figure out where I'm messing up at.  Could someone please help.

riley · Answer

-2950+124x-0.1x^2

typo**

riley · Answer

I still need help, please someone.  I just worked through this problem for the fifth time, and I'm stuck.  I can't figure out where I'm going wrong at and this is my last problem to finish. >_< uughh

gw2011 · Answer

R=130x
P=R-C
P=130x-(2950+6x+0.1x^2
P=124x-2950-0.1x^2
P=-0.1x^2+124x-2950

I used the quadratic formula to solve for x:

x=[-b+/-sqrt(b^2-4ac)]/2a

a=-0.1
b=124
c=-2950

x=[-124+/-sqrt(124^2-(4)(-0.1)(-2950)]/(2)(-0.1)

x=[-124+/-sqrt(15,376-1180)]/-0.2

x=[-124+/-sqrt(14,196)]/-0.2

x=[(-124)+/-(119.1)]/-0.2=[(-124)+/-(119)]/-0.2

x=(-124+119)/-0.2=-5/-0.2=25

x=(-124-119)/-0.2=-243/-0.2=1215 which is not a solution because 0<=x<=500

Therefore, 25 pairs of cleats need to be made to make a profit

riley · Answer

Wow, I was doing the problem the exact same way, however I see where I messed up at.  When I was using the quadratic formula to solve for x, I didn't carry over one of my signs correctly, and it screwed everything up.  Thank you so much for showing me that, I can't believe one little minor mistake like that caused so much trouble.  

Thank you again!!<3

gw2011 · Answer

You're welcome.  I'm glad I could help.