SOLUTION: A company that manufactures bikes has a fixed cost of $100.00. It costs $100.00 to product each bike. The selling price per bike is $300.00 1. write the cost function, C 2. w

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A company that manufactures bikes has a fixed cost of $100.00. It costs $100.00 to product each bike. The selling price per bike is $300.00 1. write the cost function, C 2. w      Log On


   

Question 56258: A company that manufactures bikes has a fixed cost of $100.00. It costs $100.00 to product each bike. The selling price per bike is $300.00
1. write the cost function, C
2. write the revenu function, R
3. determine the breat-even point. Describe what this means.
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
A company that manufactures bikes has a fixed cost of $100.00. It costs $100.00 to produce each bike. The selling price per bike is $300.00
1. write the cost function, C
C(x)=mx+b, where m is the cost per bike and b is the fixed price.
C(x)=100x+100
2. write the revenu function, R
R(x)=kx, where k is the selling price per bike.
R(x)=300x
3. determine the breat-even point. Describe what this means.
The break even point is when C(x)=R(x)
100x+100=300x
-100x+100x+100=300x-100x
100=200x
100/200=200x/200
1/2=x
This makes me think that perhaps you typed the problem incorrectly. Because according to this, the company breaks even if it sells half a bike. I would round that up to 1. Is the fixed cost=to the cost per bike?
Happy Calculating!!!!

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
>A company that manufactures bikes has a fixed cost of $100.00. 
It costs $100.00 to product each bike. The selling price per bike
is $300.00 

Are you sure you copied all those numbers right?  I doubt it. Wasn't
the fixed cost more than $100, perhaps $10000 or more? Only $100 for
fixed cost is awfully cheap.

But anyway, taking it as you have it:

1. write the cost function, C

Let x = the number of bikes bought and sold 

Cost function = Cost for producing x bikes + Fixed cost
       |                 |                       |  
      C(x)    =        $100x               +   $100

         C(x) = 100x + 100 
         

2. write the revenue function, R

Revenue function = the money obtained from selling x bikes
         |                         |
       R(x)      =               $300x 

         R(x) = 300x


3. determine the break-even point. Describe what this means.

This is the number of bikes, x, that must be sold to just break even,
with no profit at all, and no loss at all.  This when the total amount
spent to produce the bikes is exactly equal to the total amount taken
in from the sales of the x bikes,  To find this we put C(x) equal to 
R(x), and solve for x

        C(x) = R(x)

  100x + 100 = 300x

Solve that and get x = .5, rounded up to 1 bike, the break even point. 

So they only have to manufacture and sell one bike to more than break 
even. This is what is so unrealistic about the problem.  If the fixed 
cost were $10000 instead of a mere $100, then the break-even point would
have been 50 bikes, which is more realistic than just one measly bike.

Edwin