Question: A rectangular package has a combined length and girth (perimeter of a cross section) of 108 inches (see figure). (a) Write the volume V of

A rectangular package has a combined length and girth (perimeter of a cross section) of 108 inches (see figure).

(a) Write the volume V of the package as a function of x. What is the domain of the function?
(b) Use a graphing utility to graph the function. Be sure to use an appropriate window setting.
(c) What dimensions will maximize the volume of the package? Explain.

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a V l w h x y x x 2 y where 4x y 108 So y 108 4x and V x 2 108 4x 108x 2 4x 3 Domain 0 x 27 b c The dimensions that will maximize the volume of the package are 18 18 36 From the graph the maximum volume occurs when x 18 To find the dimension for y use the equation y 108 4x y 108 4x 108 ... View full answer

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