Lexus H.

asked • 06/13/15

Break even point!! Help!!!

Scenario with formulas:

Cost Function C(Q)= 8q+3200
Revenue Function R(Q)= -10p^2+850p ( in terms of q,  (1/10q^2)+85q ...? I think?)
 
Find the break even point(s) for this scenario. Identify the ticket price(s) that will produce the break-even point(s) needed!
 
I know break even points are setting revenue=cost. But I only get one answer :(

Stephanie M.

tutor
The reason you haven't gotten an answer to your question is that there are a lot of problems with it as it's currently formulated...
 
First, when you write C(Q), that means the thing that follows is an expression in terms of Q. But there's no Q in the cost function. In fact, there's no Q anywhere. So, we have no idea what Q stands for, and naming the equation C(Q) doesn't make sense.
 
We could maybe assume that you meant to capitalize the q, but that doesn't explain why the next function, R(Q), is also not a function in terms of Q. It's not even a function in terms of q. It's in terms of p.
 
You do give a possible expression for R(Q) in terms of q, which still isn't in terms of Q, but since there's no q in the original function, there's no way to solve it for q unless you have some way of converting between p and q. Unfortunately, there's nothing you can plug in for p to make -10p2 = (1/10)q2 besides p = q = 0, since otherwise the left-hand term is always negative and the right-hand term is always positive. So it's unclear how you got that "in terms for q" equation for many different reasons.
 
Your goal with this problem will be to set C(Q) = R(Q) and solve for Q (although it seems like you may want to solve for q here instead). It sounds like you know that and have found an answer, which is fine. You should have found two answers, since R(Q) is a quadratic, but it's possible your two answers equal each other.
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06/13/15

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Stephanie M. answered • 06/13/15

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Ignoring the problems with your question, I'll use:
 
C(q) = 8q + 3200
R(q) = (1/10)q2 + 85q
 
 
 
Set the equations equal to each other:
 
C(q) = R(q)
8q + 3200 = (1/10)q2 + 85q
80q + 32000 = q2 + 850q
0 = q2 + 850q - 80q - 32000
0 = q2 + 770q - 32000
 
 
 
Use the Quadratic Formula with a = 1, b = 770, and c = -32000:
 
q = (-b ±√(b2 - 4ac)) / (2a)
q = 39.53, -809.53
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Lexus H.

Oh yay! That's what I ended up solving for as well! My question with that is though, a break even point is in some way where they intercept. 
 
So how would I go about finding the second part of the coordinate for these? And to test for the price, I just input each if these values into the R(q) function correct?
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06/13/15

Stephanie M.

tutor
You can find the second part of each coordinate by plugging q = 39.53 and q = -809.53 into either R(q) or C(q). You've got about 5 different variables, though, and I don't know what most of them stand for (Q, q, or p), so it's hard to know what to suggest.
 
Probably, q stands for number of tickets sold or something like that. So we should probably ignore q = -809.53, since you can't sell a negative amount of tickets. Plugging that in:
 
C(39.53) = 8(39.53) + 3200 = 3516.24
 
So, the break-even point occurs at (39.53, 3516.24), when approximately 40 tickets have been sold and the cost/revenue are both $3,516.24.
 
 
 
In terms of the ticket prices, again, it's really hard to know what to plug in since I don't know what your variables stand for. Perhaps p stands for price, in which case you may want to do something like plug the revenue 3516.24 in for R(Q) and solve for p. Or, it may be that you want to do something as simple as divide the revenue 3516.24 by the number of tickets sold to find ticket price.
 
 
 
I want to emphasize that this is mostly guess-work... I'm making a whole lot of assumptions about your problem based on not much information. And, like I said in my comment above, it really doesn't seem like your expression for R(Q) in terms of q is quite right, so it's likely some calculation error has already occurred. I hope this at least helps point you in the right direction!
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06/13/15

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