Blog: An open-top box with a square base is to be constructed from two types of materials, one for the bottom and one for the sides. The volume of the...

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There is one bottom with the area $\displaystyle{{x}}^{{2}}$ square feet. Its cost is $\displaystyle{4}{{x}}^{{2}}$ Pesos. There are also four sides, each of them is a rectangle with one side of the length x and other with the length y. Therefore their combined area is $\displaystyle{4}{x}{y}$ and the cost is $\displaystyle{3}\cdot{4}{x}{y}={12}{x}{y}$ Pesos.

The volume of a box is $\displaystyle{x}\cdot{x}\cdot{y}={{x}}^{{2}}{y}={9}$ cubic feet. From this equation we can express $\displaystyle{y}=\frac{{9}}{{{x}}^{{2}}}$ feet. This is the answer for...

Hello!

The volume of a box is $\displaystyle{x}\cdot{x}\cdot{y}={{x}}^{{2}}{y}={9}$ cubic feet. From this equation we can express $\displaystyle{y}=\frac{{9}}{{{x}}^{{2}}}$ feet. This is the answer for the first question.

The total cost of the materials is

$\displaystyle{4}{{x}}^{{2}}+{12}{x}{y}={4}{{x}}^{{2}}+{12}{x}\cdot\frac{{9}}{{{x}}^{{2}}}={4}{{x}}^{{2}}+\frac{{108}}{{x}}$ (Pesos).