Maximixing revenue

[GreenBunny1]

An oil producing country can sell 7 million barrels of oil a day at a price of $90 per barrel. If each $1 price increase will result in a sales decrease of 100,000 barrels per day, what price will maximize the country's revenue? How many barrels will it sell at that price?

This is how I set it up:

x=each $1 price increase

P(X)=90+X q(X)=7-100,000X

R(X)=(90+X)(7-100,000X)

Am I doing this right so far?

 

[soroban]

Hello, GreenBunny1!

You were off to a good start.
Be careful with the numbers.

An oil producing country can sell 7 million barrels of oil a day at a price of $90 per barrel.
If each $1 price increase will result in a sales decrease of 100,000 barrels per day,
what price will maximize the country's revenue?
How many barrels will it sell at that price?

\(\displaystyle x \,=\,\text{each }\$1\text{ increase}\)

\(\displaystyle P(x) \:=\:90+x\)

\(\displaystyle Q(x) \:=\:\color{red}{7,\!000,\!000} - 100,\!000x\)

\(\displaystyle R(x)\:=\: (90+x)(7,\!000,\!000-100,\!000x)\)