# College Algebra, NOT Calculus (derivatives).

College Algebra, NOT Calculus (derivatives). United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000 cubic inches. Initially, they would like to know the dimensions of such a box with the minimum surface area. They are considering creating the box with a reinforced bottom. The box would be made out of a cardboard material costing 1 cent per square inch to build the walls and top, however the bottom would be constructed with stronger material, costing 2 cents per square inch to build. How do the dimensions of the box having the minimum surface area compare to the dimensions of the reinforced box which costs the least?

Imagine you have been contracted to solve this problem. That is, someone is paying you to provide them with an analysis of the problem. Imagine that your solution will be submitted to a group of management-level employees at United Parcel Service and they will use your analysis when making a decision.

With this in mind, your submission should include the following:

a) A discussion (one paragraph or so) on what the problem is asking. Someone who has never seen the original problem should be able to tell what the problem was and exactly what is being asked after reading this paragraph.

b) A short discussion on your plan for solving the problem. This should include definitions of each of the variables as well as an explanation of the equation you are building and using to solve the problem.

c) A step by step solution of the problem. This should be clear and easy for a reader to follow (even if the reader may not be well-versed in mathematics). This means you should justify your steps in solving the problem.

d) A clear statement of the solution to the problem and answers to any questions.

e) Any implications of the solution

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