For a company manufacturing iPADs the cost and revenue equations (in dollars) are given by... (below)
where x is the weekly production output of iPADs. If production is increasing at a rate of 4 iPADs per week when 360 iPADs are produced, find the rate of increase in profit.

Question

For a company manufacturing iPADs the cost and revenue equations (in dollars) are given by... (below)
where x is the weekly production output of iPADs. If production is increasing at a rate of 4 iPADs per week when 360 iPADs are produced, find the rate of increase in profit.

thatonegirl_ · Answer

$$C(x)=200+30x$$
$$R(x)=300x-\frac{ x^2 }{ 40 }$$

solomonzelman · Answer

What is C(x) and R(x) ?

thatonegirl_ · Answer

I am assuming cost and revenue

solomonzelman · Answer

The profit is revenue-cost. (Right?)
(I will denote profit by $P(x)$.)

$P(x)=R(x)-C(x)$

thatonegirl_ · Answer

Yup looks good

solomonzelman · Answer

So, subtract, and that would be the function that models your profit.

solomonzelman · Answer

Then, if you want to get the rate of increase in profit, just differentiate (once).

thatonegirl_ · Answer

Okay gimme a min

thatonegirl_ · Answer

Should i be using the quotient rule?

solomonzelman · Answer

First, tell me what is your $P(x)$ ?

solomonzelman · Answer

(no, I don't think you should)

thatonegirl_ · Answer

$$\frac{ -x^2+1080x-8000 }{ 40 }$$

thatonegirl_ · Answer

i combined them all. Could i just multiply by 40 to get rid of the denominator?

solomonzelman · Answer

$\displaystyle P(x)=270x-\frac{x^2}{40}-200$

solomonzelman · Answer

You don't need to combine.

solomonzelman · Answer

Just differentiate with the Power Rule, term by term.

thatonegirl_ · Answer

is this with respect to time or to x?

solomonzelman · Answer

Oh, with respect to x, of course.

thatonegirl_ · Answer

oh okay

thatonegirl_ · Answer

hmm so how do u take the derivative of x^2/40?

solomonzelman · Answer

How do you differentiate $\displaystyle ax^2$, or $\displaystyle \frac{1}{40}x^2$ ?

thatonegirl_ · Answer

ohh ty lol

thatonegirl_ · Answer

okay so $$P'(x)=270-\frac{ 1 }{ 20 }x$$

solomonzelman · Answer

Yes.

thatonegirl_ · Answer

Okay so then what?

solomonzelman · Answer

I think we found the rate of increase in profit, haven't we?

thatonegirl_ · Answer

my answers choices are
$1007per week
$1006per week
$1008per week
$1010per week
$1009 per week

solomonzelman · Answer

I might have gone wrong somewhere:(

thatonegirl_ · Answer

If it helps at all we are learning about derivatives with respect to time >.<

thatonegirl_ · Answer

Idk the fancy name for it lol oops

solomonzelman · Answer

Apparently the rate of change of the profit is there, but I don't know how to relate that to the verbal part of the problem.

solomonzelman · Answer

(I am not a very patient reader, perhaps. Sorry.)

thatonegirl_ · Answer

Ah okay thanks anyways! I appreciate your time and effort!! :)