Question

Mike repairs televisions. His revenue equals R(h)=25+30h dollars for every h hours he spends repairing television. His overhead cost equals C(h)=5h2-10 dollars.
After how many hours does he break even?

Answer 1

Are you allowed to graph this, or do you need to solve it out algebraically?

Answer 2

Also, is the 2 in 5h2 supposed to be an exponent?

Answer 3

well, i don't know

Answer 4

We'll do it algebraically then since that's what most teachers prefer.

Answer 5

okay

Answer 6

And the question on the 5h2?

Answer 7

Is the 2 a exponent?

Answer 8

oh yes it is

Answer 9

Okay then, here's what we need to do...The point where it breaks even is going to be found with profit=0 or when the revenue is the same as the cost.
Do you know how to write a function for that?

Answer 10

I'm not sure

Answer 11

whoops sorry

Answer 12

It's alright. Mine keeps going in and out as well

Answer 13

Let me ask you this...Breaking even would be at a point where the worker receives no profit nor does he lose any money. Do you agree with that?

Answer 14

Why is that?

Answer 15

Because, he can't break even, if he did or didnt lose money wouldnt possibility be correct

Answer 16

Well lets consider this...The definition of breaking even is "to reach a point in a business venture when the profits are equal to the costs".
Do you agree that 1 + 1 = 0?

Answer 17

no 1+1 does not equal 0

Answer 18

Lol So sorry. I meant 1-1=0

Answer 19

We both know that 1-1=0.
With that being said, if our "break even point" is where the cost equals the profit, then we would receive no profit, nor would we lose any money.
Does that make sense?

Answer 20

yes

Answer 21

So back to what I said earlier, "Breaking even would be at a point where the worker receives no profit nor does he lose any money." Do you understand why that is actually correct?

Answer 22

If you don't, just let me know.

Answer 23

okay

Answer 24

Okay as in you don't?

Answer 25

no i do

Answer 26

I'm trying to figure out how many hours is asking me

Answer 27

Okay. Excellent.
Now that we know that our cost and revenue must be the same in order to reach our break even point, we know that
(Revenue) - (Cost) = 0
So R(h) - C(h) = 0
(25+30h) - (5h^2-10) = 0

Answer 28

okay,so we have that just how are we going to solve it?

Answer 29

(25+30h) - (5h^2-10) = 0

Simplify and get...
-5h^2 + 30h + 35 = 0

Make sense so far?

Answer 30

Don't worry, I'm getting there.

Answer 31

yes, it makes sense

Answer 32

Okay, no we are going to use the quadratic formula to solve for the 0's in our function...
\[h=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]

Answer 33

\[h= \frac{ −(30)±\sqrt{(30)^2−4(-5)(35)}}{ 2(-5)}\]

Answer 34

Can you solve that?

Answer 35

yes

Answer 36

Go for it. :)

Answer 37

-10 +/- ^200/-10

Answer 38

Um, that's not what I got. Let me check again.

Answer 39

yea, i think idk

Answer 40

\[h=\frac{ −(30)±\sqrt{(30)^2−4(−5)(35)} }{ 2(−5) }\]
\[h=\frac{ −30±\sqrt{30^2-700} }{ -10 }\]
\[h=\frac{ −30±\sqrt{900-700} }{ -10 }\]
\[h=\frac{ −30±\sqrt{1600} }{ -10 }\]
\[h=\frac{ −30±40 }{ -10 }\]

Answer 41

Just a moment...

Answer 42

My power is giving out here. There's a bad storm happening

Answer 43

uh oh, not here until tomorrow, cause i'm in Florida

Answer 44

\[h=\frac{−30±40}{−10}\] Because there's a ± sign, we can solve this 2 ways...
\[h=\frac{−30-(40)}{−10}\] which -30 - 40 = -70 and -70/-10 = 7 so one of your zeroes is h=7

The other is... \[h=\frac{−30+(40)}{−10}\]which -30 + 40 = 10 and 10/-10 = -1 so your other zero is h=-1

Answer 45

Can you tell which zero (aka the amount of hours) is the correct answer for this problem?

Answer 46

i would with 7h

Answer 47

Correct. You can't have a negative amount of hours, so -1 makes no sense.
Therefore, 7 hours would be your break even point.

Answer 48

Thank you so much

Answer 49

You can see this on a graph if you go to www.desmos.com/calculator, and in one of the spaces put (25+30x)-(5x^2-10).
You'll see that -1 and 7 are the x-intercepts.

Answer 50

You're very welcome! :D

Answer 51

well i gtg bye bye and thanks for helping me

Answer 52

You're welcome and goodnight.