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TANAPMATH$710\mathrm{.}5\mathrm{.}017.$

Product Design The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular and will have an internal volume of $2\mathrm{.}4f{t}^3.$ For aesthetic reasons, the design team has decided that the height of the cabinet is to be $1\mathrm{.}5$ times its width. If the top, bottom, and sides of the cabinet are constructed of veneer costing $45\frac{c}{f}{t}^2$ and the front $($ignore the cutouts in the baffle$)$ and rear are constructed of particle board costing $15\frac{}{f}{t}^2,$ what are the dimensions of the enclosure that can be constructed at a minimum cost?

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