Average Cost 2

[harpazo]

Suppose that the government imposes a $1000 per day tax on the bicycle manufacturer so that the daily cost C of manufacturing x bicycles is now given by C(x) = 80x + 6000. Now the average daily cost is given by (x). How many bicycles must be produced each day for the average cost to be no more than $100?

Solution:

Again, the average cost = C(x)/x.

Why is C(x) over x the average cost? Define average cost (in words).

Again, set 100 = to the average cost.

Why must we set 100 to the average cost?

100 =( 80x + 6000)/x

80 + (6000/x)

Calculate x.

20 = 6000/x

So, x = 300 should be the number of bicycles produced.

 

[MarkFL]

If you had waited to post this problem until getting help with the first, you would find the help I gave there applies equally well to this problem, since only 1 parameter has been changed.

 

[harpazo]

If you had waited to post this problem until getting help with the first, you would find the help I gave there applies equally well to this problem, since only 1 parameter has been changed.

Ok. Thanks.

 

[Otis]

... average daily cost is given by (x) ...

... x = 300 should be the number of bicycles produced ...

Symbol x cannot represent both cost and quantity.

 

[Dr.Peterson]

I searched for problems with the same wording, and found it all over the place; some have that "(x)", and others have the correct C(x)/x or equivalent. I suspect the former arises from copying out of software that represents the C(x)/x in an odd way that doesn't fully copy. Here is an example of what one such problem actually looks like on screen:

Probably the [MATH]\overline{C}[/MATH] and [MATH]\frac{70x+4400}{x}[/MATH] are images that don't copy, so students who copy without paying attention get "given by (x) = ".

This is yet another reason not to try to learn from these sites that post students' copies of problems without checking them out carefully, rather than one that posts actual lessons with its own properly formatted problems.