The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section. Suppose the strength of an oak beam is 65, when the beam is 2 inches wide and 6 inches deep. Determine the strength, S, of the largest rectangular beam that can be cut from a 26-inch-diameter oak tree, given that the beam must be 6 inches wide. Remember y is proportional to a if there is a constant k such that
y = kx. The constant k is known as the constant of proportionality.