# A tent is constructed in the shape of a pyramid with square base and four faces; each face is

in the shape of an isosceles triangle. The tent is made by cutting away a triangle from each side of a

6 ft x 6 ft silicon-coated polyester and bending up the the resulting triangles to form the walls of

the tent. A steel pole, perpendicular to the base, is placed in the center of the tent for support.

**(PICTURE OF FIGURE ATTACHED BELOW)**

**a) Show that the function to be optimized is** V(x) = $31 x_{2}18−32 x $

where x represents the side length of the square base. Provide an appropriate domain for V .

**Fully justify every step of the derivation of the function.**

b) Find the maximum volume the tent can have. **Fully justify your answer.**

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