Question 1096736: Can someone please explain me how to solve this? Thank you.
A company is planning to manufacture mountain bikes. The fixed monthly cost will be $200,000 and it will cost $200 to produce each bicycle. Complete parts (a)-(c).
a) Find the linear cost function.
b) Find the average cost function.
c) Find the horizontal asymptote of the graph of the average cost function. Explain what the asymptote means in this situation.
_________________________________________
a)Write the cost function, C, of producing x mountain bikes per month.
C(x)=?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the linear cost function is y = 200,000 + 200 * x
the average cost function is y = (200,000 + 200 * x) / x
the horizontal asymptote of the average cost function is 200.
as the number of bikes sold becomes greater and greater, the effect of the fixed cost becomes less and less until it becomes almost 0, at which time you are effectively dealing with the incremental cost of production only.
c(x) = 200,000 + 200 * x.
that's your cost function.
when you set y = c(x), they mean the same thing.
y = 200,000 + 200 * x is the same equation as c(x) = 200,000 + 200 * x.
when you sell 1 bike, the average cost is (200,000 + 200 * 1) / 1 = 200,200.
when you sell 1,000,000 bikes, the average cost is (200,000 + 200 * 1,000,000) / 1,000,000) = 200.2 per bike.
when you sell 1,000,000,000 bikes, the average cost is (200,000 + 200 * 1,000,000,000) / 1,000,000,000 = 200.0002
of course, this is highly theoretical because nobody sells 1,000,000,000 bikes each month.
not that i know of, anyway.
however, the average cost of a bike sold gets closer and closer to the incremental cost of 200, the more bikes you sell in a month.
|
|
|
