SOLUTION: The total weekly revenue earned at Royal Ruby Retailers is given by following function where p is the price RRR charges per ruby. Use this function to determine: First, the wee

Question 215077This question is from textbook finite mathematics
:
The total weekly revenue earned at Royal Ruby Retailers is given by following function where p is the price RRR charges per ruby. Use this function to determine: First, the weekly revenue to the nearest dollar, when the price is set at $20/ruby; Second, find the weekly revenue, to the nearest dollar, when the price is set at $200/ruby; Third, find the price RRR should charge in order to obtain a weekly revenue of $1200. (if you get negative answers do not assume that it is wrong!)
R(p) = - 4/3 p^2 + 80p
The weekly revenue when the price is set at $20/ruby is $.
The weekly revenue when the price is set at $200/ruby is $.
RRR should charge $ per ruby to obtain a weekly revenue.This question is from textbook finite mathematics

Answer by checkley77(12569) (Show Source):
You can put this solution on YOUR website!
R(p) = - 4/3 p^2 + 80p
R(20)=-4/3*20^2+80*20
R(20)=-4/3*400+1600
R(20)=-1,600/3+1,600
R(20)=-533.33+1,600
R(20)=$1,067 WEEKLY REVENUE WHEN RUBYS ARE $20.
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R(200)=-4/3*200^2+80*200
R(200)=-4/3*40,000+16,000
R(200)=-160,000/3+16,000
R(200)=-53,333+16,000
R(200)=-$37,333 WEEKLY LOSS WHEN RUBYS ARE $200.
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1,200=-4/3P^2+80P
4P^2/3-80P+1200=0
4P^2-240P+3600=0
4(P^2-60P+900)=0
4(P-30)(P-30)=0
P-30=0
P=$30 IS THE RUBY PRICE TO OBTAIN A WEEKLY REVENUE OF $1,200.