label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

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.

Jul 15th, 2015

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

Jul 15th, 2015

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

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Jul 15th, 2015
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Jul 15th, 2015
Oct 18th, 2017
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