Minimizing Packaging Costs A rectangular box $isto$ have a square base and a volume $of81f{t}^3.If$ the material for the base costs $$\frac{0\mathrm{.}56}{f}{t}^2,$ the material for the

sides costs $$\frac{0\mathrm{.}15}{f}{t}^2,$ and the material for the top costs $$\frac{0\mathrm{.}34}{f}{t}^2,$ determine the dimensions $(inft)of$ the box that can $be$ constructed $at$ minimum cost. $(Referto$ the

figure below.$)$

$x=1$

$ft$

$y=$

$ft$