SOLUTION: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find

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Question 166178: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is $8 for each football.
This is the answer that it is showing r(q)= -150q^2 + 3000q, 14,400
Can you show me how they got this answer please.

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
The number of footballs sold is,
N=3000-150q
The price for each football is q.
The total revenue is just the number of footballs sold multiplied by the price of each football.
R%28q%29=%283000-150q%29q
R%28q%29=-150q%5E2%2B3000q
.
.
.
When q=$8, then
R%28q%29=-150q%5E2%2B3000q
R%288%29=-150%288%29%5E2%2B3000%288%29
R%288%29=-150%2864%29%2B24000
R%288%29=-9600%2B24000
R%288%29=14400
The weekly revenue when footballs are $8 a piece is $14,400.