The total weekly revenue earned at Royal Ruby Retailers is given by R(p) = ? 4/3

Question

The total weekly revenue earned at Royal Ruby Retailers is given by R(p) = ? 4/3p^2 + 80p p2 + 80p where p is the price (in dollars) RRR charges per ruby. Use this function to determine the following. (a) the weekly revenue, to the nearest dollar, when the price is set at $40/ruby. (Round your answer to the nearest integer.) R(p) = $ (b) the weekly revenue, to the nearest dollar, when the price is set at $400/ruby. (Round your answer to the nearest integer.) R(p) = $ Interpret your result. Since revenue (can or cannot) be negative, we conclude that the domain of the demand function (Select--- can cannot) realistically include p = $400. (c) the price RRR should charge in order to obtain a weekly revenue of $1,200 p = $

Explanation / Answer

(a) R(p)=(4/3)p^2+80p For p=40, R(p)=(4/3)*(40)^2+80*40=(6400/3)+3200=16000/3 =5333 $ (b) R(p)=(4/3)p^2+80p For p=400, R(p)=(4/3)*(400)^2+80*400=(640000/3)+32000=16000/3 =245333 $ (c) R(p)=(4/3)p^2+80p=1200 or, p^2+60p-900=0 or, p=12.426 $

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