A postal service will accept packages only if the length plus girth is no more than 42 inches. (See the figure.) Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept?

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anonymous · Answer

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Since you didn't provide a figure, i drew something myself to illustrate how i percieve it. To find to optimal volume we must find the maximum of (x^2)(y) where 

$$x^2+y=42$$

in order to solve this problem let's rewrite y in terms of x. $$y=42-x^2$$

now, to find we volume we can write $$\left( x^2 \right)\left( 42-x^2 \right) \in 0 \le x\ \le \sqrt{42}$$

now simply finding the max of that formula will give you the maximum possible volume.