Minimum surface area box of all boxes with a square base and a volume of 100 m2 which one has the minimum surface area? (Give its dimensions.)

Solution Step 1: Consider a box having square base of width l,length l and height h Surface area of the box is the objective function A=2(l +2lh) 3 And volume is the constraint which is 100m V=l h=100m 3 The objective is to find the dimension of box of volume which is having minimum surface area Step 2: The first step is use the constraints to express the objective function A in terms of single variable For this l h=100 100 h = l2