Homework Sourseif you are to build a rectangular dumpster which uses a thic
if you are to build a rectangular dumpster which uses a thicker type of steel for the bottom of the container than for the walls. If the top will be covered by plastic doors which cost 50 total no matter what size they are, and the steel for the bottom panek costs 2 times as much per square meter as the walls. what dimensions would minimize the cost id the volume is to be equal to 8 m^3?
Solution
Say the dumpster is \'a\' m long & \'a\' m wide. Say it\'s height is \'h\' m. Volume = ha^2 = 8 Total Cost = 50 + b[2a^2 + 2h(2a)], where b is a constant TC = 50 + b[2a^2 + 2(8/a^2)(2a)] d(TC)/da = 0 4a = 32/a^2 a = 2 m h = 2 m Cuboid dimensions - 2m x 2m x 2m
