TJC Inequalities Tutorial Q10
(i)
A wooden artwork is designed to take the form of a right pyramid with square base of sides $2x$m and fixed volume $\frac{4}{3}$m$^{3}$. All its exterior faces, including the base, need to be painted. The cost per square metre of painting each of the $4$ inclined faces is twice that of painting the base. Given that the cost of painting the base is $\$p$/m$^{2}$, show that the total cost of painting the artwork is
$\$\,4p{{x}^{2}}\left(1+2\sqrt{1+{{x}^{-\,6}}}\right)$.
(ii)
Determine the possible heights the artwork may take if the budget given for the paint works is $\$16p$.
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