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Optimization Assignment - Paperwork and Video Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers with a cost effective, versatile rectangular storage container with a square base and a volume of 36 fts (see the diagram below). Each company has determined they want to use the same type of materials to construct the containers. The material for the sides and top of each container costs $2/ft2, and the material for the bottom costs $4/ft2. Lone Depot claims that the minimum cost of producing such a container with the desired volume of 36 ft' can be obtained if the dimensions of the container are 2.5 ft by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of producing such a container can be obtained if the dimensions of the container are 4 ft by 4 ft by 2.25 ft. 1. Which company's proposed dimensions are better? In other words, which will result in a lower cost of constructing each container? a) Mathematically justify your answer. For each store, you must draw at least two rectangles with labeled dimensions to represent the surfaces that you are finding the area of. b) Write a paragraph explaining your work and answer. 2. Determine whether either of these company's dimensions are the best. In other words, determine the dimensions that would minimize the cost of producing each storage container, as well as the minimum cost. a) Show all of your work as we did in-class