Register to reply 
Another maximizeby tony873004
Tags: maximize 
Share this thread: 
#1
May2006, 08:16 PM

Sci Advisor
PF Gold
P: 1,542

The demand for rubies is given by the equation
[tex] q = \frac{4}{3}p + 80 [/tex] where p is the price and q is the number of rubies sold each week. At what price should the rubies be sold to maximize weekly revenue? [tex] \begin{array}{l} R = pq \\ R = p\left( {\frac{4}{3}p + 80} \right) \\ R = \frac{4}{3}p^2 + 80p \\ \\ R' = \frac{8}{3}p + 80 \\ \\ \frac{8}{3}p + 80 = 0 \\ \\ \frac{8}{3}p =  80 \\ \\ p = \frac{{  80}}{{\left( {\frac{8}{3}} \right)}} = \frac{{  240}}{8} =  30 \\ \end{array} [/tex] To maximize weekly revenue, they should give away the rubies and $30 per rubie. (Obviously wrong. The back of the book says $30) 


#2
May2006, 08:23 PM

P: n/a

It looks like by the second derivative of R with respect to P that actually minimizes the revenue. To maximize revenue then would be to choose the highest price possible. The demand formula doesn't make sense to begin with because it implies that you sell more rubies as the price goes up on rubies, so a strange answer doesn't seem out of the question.



#3
May2006, 08:27 PM

P: 198

This doesn't make any sense.
q = 4/3p + 80 So when you increase the price you sell more rubies? In that case you would maximize weekly revenue by selling an infinite number of rubies. Either I'm not understanding you correctly, or you are missing a minus sign in that formula, try something like: q = 4/3p + 80 and see how that works. EDIT: That seems to give you the right answer, it must be a typo in the book. ~Lyuokdea 


#4
May2006, 08:33 PM

PF Gold
P: 621

Another maximize
To go along with what Lyokdea said, you also know something is wrong when you look at your equation for revenue that you're trying to maximize: R=4/3p^{2}+80p. This function clearly has no absolute maximum; only a minimum. (It's an upwardsopening parabola)



#5
May2006, 08:35 PM

Sci Advisor
HW Helper
P: 2,884

Are you sure that the first equation should not read 4/3p+80? With the equation you gave, increasing the price keeps increasing the number sold, which is weird. And notice that your function for R is concave upward..Taking the price to infinity will lead to infinite revenues! (what you found is actually the minimum). If the equation for R was 4/3p + 80 it would fix everything and make sense now. Maybe a typo in the book? Patrick 


#6
May2006, 08:37 PM

Sci Advisor
PF Gold
P: 1,542

sorry, I was blind and didn't see the negative sign. 4/3p + 80. Sorry for the inconvenience.



#7
May2006, 08:37 PM

P: 198

~Lyuokdea 


#8
May2006, 08:39 PM

Sci Advisor
PF Gold
P: 1,542




#9
May2006, 08:43 PM

Sci Advisor
HW Helper
P: 2,884

And sorry for having repeated what you said, I just saw your post after I sent mine. Regards 


Register to reply 
Related Discussions  
Maximize this  Calculus  0  
Maximize money  Social Sciences  10  
Maximize the flux  Calculus & Beyond Homework  1  
Help with Maximize  Calculus & Beyond Homework  4  
Maximize area  Calculus  2 