Help with equation

Question

Help with equation

anonymous · Answer

help me

mrnood · Answer

can you write
$$\frac{ 10+900 }{ x }$$

as 2 separate terms (each with denominator x)

mrnood · Answer

sorry - I meant
$$\frac{ 10x+900 }{ x }$$

darkbluechocobo · Answer

The average cost function for a particular business that sells toys is represented by A(x)=$$\frac{ 10x+900 }{ x }$$ where A is represented in dollars and x is the number of toys produced. In the long run, what will be the average cost to produce a large amount of toys for this company?

darkbluechocobo · Answer

aha is that what you meant

mrnood · Answer

so - write that as 2 separate terms....

darkbluechocobo · Answer

so like 10x/x and 900/x? >< im confused

mrnood · Answer

yes - that is correct

so the average cost is

$$\frac{ 10x }{ x}+ \frac{ 900 }{ x }$$

what is another way of writing the first term?

what happens to the second term if x is very large?

darkbluechocobo · Answer

well the x's cancel out so it would be 10/1 +900/x

mrnood · Answer

and what happens to the second term if x is very large?

darkbluechocobo · Answer

would it become smaller?

mrnood · Answer

very small or approximately zero

so average price = 10 + (approx. 0)

darkbluechocobo · Answer

question. 10 is the horizontal asymptote is this just a coincidence?

mrnood · Answer

did you plot this ?

it's not coincidence - you can see that the 'fixed part' of the cost (900) becomes insignificant, whereas the variable part (10x) stays the same as the number produced increases

This is typical of manufacturing industry - fixed costs such as rent, fixed staff costs etc. are liable even if the volume produced is zero.

Variable costs, such as materials, utility costs for machinery, and labour costs for manufacture increase approximately linearly with the production volume....