According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? Such a package is shown below, with x and y measured in inches. Assume y > x. What are the dimensions of the package of largest volume? X X = y Find a formula for the volume V(x) in terms of x. V(x) = cubic inches What is the domain of the function V? Note that must be positive and y > x; consider how these facts, and the constraint that girth plus length is 108 inches, limit the possible values for x. Give your answer using interval notation. Domain: Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume. Maximum Volume= Optimal dimensions: x = cubic inches and y = inches

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