Suppose you want to determine the maximum area of an isosceles triangle that has a perimeter of 30 inches (see the image below). Which function would you need to differentiate (in terms of a single variable)?

$A(a) = \answer {(1/2) (30 - 2 a) \sqrt {(30 a - 225)}}$

A company wants to fence a rectangular storage area consisting of three separate compartments of equal size (see the image below). The fencing costs $3.00 per linear foot and the company has a budget of $180 for building the storage area. Find the length (l) and width (w) of the storage area that maximizes the total area.

$w = \answer {7.5}$ and $l = \answer {15}$

We want to construct a box with a square bottom, rectangular sides, and no top. We have exactly 10 $ft^2$ of material for building the box. If we use all of the material in building the box, what is the largest volume we could enclose in the box? (Round your answer to 3 decimal places.)

$\answer {3.043} ft^3$