Can someone please help with the below question?

Calculus
Tutor: None Selected Time limit: 1 Day

revenue is found with he equation r=pq where p is the price charged and q is the quantity sold. If the price function is changing at a rate of 10 cents per day and the quantity sold is changing at -2 items per day. How is the revenue per day changing if the price is currently at $5 and the quantity sold is 100 items?

Jul 15th, 2015

Hello!

Denote the number of days passed as n, n>=0. Then p=p(n)=5+0.1n and q=q(n)=100-2n. Thetefore r=r(n)=(5+0.1n)*(100-2n)=500+10n-10n-0.2n^2=500-0.2n^2.

This function is relatively simple. Its graph is a parabola branches down with the vertex (maximum) at n=0 (r(0)=500$). It has a root at sqrt(500/0.2)=50 (days). I.e. revenue descends and after 50th day becames negative.

Please ask if anything is unclear.
Jul 15th, 2015

but How is the revenue per day changing and by what amount

Jul 15th, 2015

Is the answer zero?

Jul 15th, 2015

Revenue per day decreases, the rate of decrease is not constant.
I.e. the amount of decrease is different each day.

Jul 15th, 2015

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Jul 15th, 2015
...
Jul 15th, 2015
Dec 7th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer