you have been tasked to build a rectangular box. the top and bottom are to be built out of 2 cm thick aluminum. the density of aluminum is 2.7 g per cm3, and the cost $1.2 per kg. the front and back walls are to be build out of 1 cm thick stainless steel. the density of stainless steel is 7.5 g per cm3, and the cost $1.2 per kg. finally, the 2 remaining walls are to be built out of 1 cm thick copper. the density of copper is 9.0 g per cm3, and the cost $9 per kg. find the measurements and total price of the least expensive such box that has volume 8 m3. (ignore any issues of the sides not fitting perfectly together because the width is not zero.)