A company selling widgets has found that the number of items sold, x, depends upon the price, p at which they're sold, according to the equation x=80000/(0.4p+1)^2

Question

Due to inflation and increasing health benefit costs, the company has been increasing the price by $0.03 per month. Find the rate at which revenue is changing when the company is selling widgets at $6 each.

Revenue is decreasing by how much dollars per month??

Answer 1

I did this for you yesterday. Did you even bother to check?
revenue = price * quantity, so the revenue r(p) is
r = p*80000/(0.4p+1)^2 = 2,000,000p/(2p+5)^2
dr/dt = -2,000,000 (2p-5)/(2p+5)^3
so plug in your numbers.

Answer 2

i did check, but it wrong. Maybe I'm plugging in the wrong numbers? I'm also confused on how you got the revenue equation. Would it be possible for you to show me step by step? i really do appreciate the help!

Here is what I did based on what you told me.
-2,000,000(2(6)-5)/(2(6)+5)^3
which equals to -2849.58274

What am I doing wrong? is it the numbers I'm plugging in? or the calculation? I'm confused.

Answer 3

Ok actually i got it. Thank you so much! i just had to multiple my previous answer with the dp/dt.

(-2849.58274)(0.03)

So it is decreasing by $85.4874822 dollars per month.

Answer 4

What were the steps to get the final equation?
r = p*80000/(0.4p+1)^2
(did you have to multiply the top and bottom of the fraction by 25)
r = 2,000,000p/(2p+5)^2
dr/dt = -2,000,000 (2p-5)/(2p+5)^3