a designer is making a metal box in the shape of a rectangular prism. the sum of its length, width, and height is 11 imches. the length must be 4 inches longer than the width. if the box has the maximum volume possible, what would the height and volume be?

The net of the rectangular prism can be drawn in the shape of a "t", with the top bar of the "t" consisting of 3 panels, each 12 cm high. the left and right panels are 9 cm wide, and the central one is 5 cm wide. the stem of the "t" consist of 3 panels below the central panel of the top bar. those three panels are 5 cm wide and alternate between 9 cm high and 12 cm high.