For a motion picture image it may be necessary to change every pixel in the image as many as thirty times per second, although usually the amount of change is somewhat smaller. This means that without data compression or other tricks that a large number of pixel values must be moved from main memory to video memory each second to produce moving video images. Assume a video image on the screen of 1 1/2′′ × 2′′, with a pixel resolution of one hundred forty dots per inch and a frame rate of thirty per second. Calculate the required data transfer rate necessary to produce the movie on the screen. Do the same for an image of 3′′ × 4′′.