MATH116 Lecture Notes - Lecture 17: Pythagorean Theorem
9 Dec 2015
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Tutorial solutions 8: a closed rectangular container with a square base is to have a volume of 2000 cubic centimeters. It costs twice as much per square centimeter for the top and bottom as it does for the sides. Find the dimensions of the container of least cost. Since there is a square base, the width and length are the same, call them w. call the height: since the volume is given to be 2000, we can set 2000 = w2h. The total cost will be proportional to the surface area of the sides (4hw) plus twice the surface area of the top (w2) and bottom (w2), since it costs twice as much for the top and bottom. Hence the total cost is proportional to c = 2 (2w2) + 4(hw) = 4(w2 + hw). Since 2000 = w2h, we can isolate h to get h = 2000.
