1. You’ve been hired by a company that makes rectangular storagecontainers. Each container has a
square base and each container must have a volume of 10 m^3. Thematerial for the base and top costs $6/m^2 and the material for thefour sides costs $4/m^2. Find the dimensions of the container thatminimize the cost of each container.
2. You want to impress your boss by creating a general strategyfor finding the dimensions of the cheapest
storage container given that the cost of material for the topand bottom is p dollars per square meter and the cost of thematerial for the sides is q dollars per square meter. As before,the storage container is rectangular, has a square base, and musthave a volume of 10 m^3. Your dimensions will involve p and q.
For each part, you want to prove to your bossthat these dimensions actually do minimize the cost.
Accordingly, you include an argument as to why these dimensionsMUST minimize the cost.
