a. A rectangle is constructed with one side on the positive x-axis, one side on the positive y-axis, and the vertex opposite the origin on the line y = 10 - 2x. What dimensions maximize the area of the rectangle? What is the maximum area?

b. Is it possible to construct a rectangle with a greater area than that found in part (a) by placing one side of the rectangle on the line y = 10 - 2x and the two vertices not on that line on the positive x- and y-axes? Find the dimensions of the rectangle of maximum area that can be constructed in this way.