The demand for rubies is given by the equation(adsbygoogle = window.adsbygoogle || []).push({});

[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)

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