An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length.

An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length. The length of the box is labeled x in the picture. You have 100 in² of cardboard to use. Find the length x and the height y that maximize the volume of the box.

(a.) Find a formula for the volume V in terms of x and y.

(b) Use the constraint given by the amount of cardboard available to rewrite your formula for V above in terms of a function of x alone.

(c) Find the dimensions, x and y, that result in the maximum volume.

(d) Justify that the values x and y given in (c) yield a maximum using either the First or Second Derivative Test.

Expert Solution

Colby Messinger answered 2 years ago

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