Average cost problem

any812

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It cost a company $50,000 to begin production of a good, plus $13 for every unit of the good produced. Let X be the number of units produced by the company.

Find a formula for C(X), the total cost for the production of X units of the good.
50,000 + 13x = C(x)

Find a formula for the company's average cost per unit, A(x).
??? i do not understand how to find this...

would it be
(13x)/x = A(x)

i do not understand this question because i am in trig and my teacher just gives this problem out of nowhere so i don't get it.


Thanks.
 
It cost a company $50,000 to begin production of a good, plus $13 for every unit of the good produced.

Let X be the number of units produced by the company.

Find a formula for C(X), the total cost for the production of X units of the good.

50,000 + 13x = C(x)

Find a formula for the company's average cost per unit, A(x).

??? i do not understand how to find this...

would it be

(13x)/x = A(x)

i do not understand this question because i am in trig and my teacher just gives this problem out of nowhere so i don't get it.

Hi any812:

Sounds like your teacher expects the students to have already learned what an average is. (That topic is generally covered in pre-algebra.)

Your formula for C(x) is correct.

(Note the red Xs above. Don't switch back and forth between x and X because those symbols are not the same. Use one or the other.)

The average cost-per-unit is simply (total cost of producing x units)/(total number of units produced)

Well, you already have the "total cost of producing x units". That's C(x).

And the "total number of units produced" is what symbol x represents.

Therefore, A(x) = C(x)/x

What does that work out to be?

Cheers :cool:
 
It cost a company $50,000 to begin production of a good, plus $13 for every unit of the good produced. Let X be the number of units produced by the company.

Find a formula for C(X), the total cost for the production of X units of the good.
50,000 + 13x = C(x)

Find a formula for the company's average cost per unit, A(x).
??? i do not understand how to find this...

would it be
(13x)/x = A(x)

i do not understand this question because i am in trig and my teacher just gives this problem out of nowhere so i don't get it.


Thanks.
First, see quaid's response above.

Second, this problem may be given for the purpose of showing that economic theory sometimes uses the language of trig for the sake of conciseness. I suspect that that is why the problem was given.

Graph total cost as a function of quantity produced, with cost as the vertical axis and units produced as the horizontal axis. (The resulting graph will be in the first quadrant and be everywhere above the horizontal axis if there are any fixed costs.) Now pick any positive quantity and graph a straight line from the origin to some point on the graph of total cost. That line makes an angle with the horizontal axis. Average cost is the tangent of that angle. As I say, economists sometimes make such a graph and use trigonometric notation for purposes of abstract explication and conciseness, but absolutely no one consciously uses trigonometry as a practical tool for calculating average cost.
 
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