hy the gift According to the shipping regulation of a may not exceed 124 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 What are the dimensions of the package of largest volume a Suppose a box has two square ends and other faces are rectangles Let a represent the length of one side of the square end and y the length of the longer side Draw the box and label the sides b Find a formula for the volume of the box in terms of x and y V c The problem statement tells us that the parcel s girth plus length may not exceed 124 inches In order to maximize volume we assume that we will actually need the girth plus length to equal 124 inches What equation does this produce involving and y d Solve the equation you found in c for one of a or y whichever is easier e Now use your work in b and d to determine a formula for the volume of the parcel so that this formula is a function of a single variable Simplify your answer V f Over what domain should we consider this function Note that both x and y must be positive how does the constraint that girth plus length is 124 inches produce intervals of possible values for x and y g Find the absolute maximum of the volume of the parcel on the domain you established in f and hence also determine the dimensions of the box of greatest volume C y in in