MAT 125 Survey of Calculus - Optimization Project Overview Projects extend your problem-solving experience and provide opportunities to explore applications more deeply. They also provide an interesting and engaging way to work and investigate ideas collaboratively with other students. Lastly, projects give you the experience of communicating your work in writing in a clear and logical form. Written communication skills are essential in the business world. Scenario The consultant company "Business Pro" you currently work for provides analysis and projections for clients to apply in their businesses. Business Pro advises their clients on how to reduce costs and maximize profits. Your manager, George Big, sends you the following email. We have a client asking for our recommendations on the best size and shape of containers for their product. Their requirements are as follows: - The containers will hold 10,000 cubic centimeters (10L). - Containers will be made from aluminum sheet with a thickness of 0.03 cm. - there are two options for the shape of the containers: - Option 1: closed cylinders. - Option 2: closed boxes with a square base. Some considerations to consider: - the cost of production of a cylindrical container is $2 per cylinder. - the cost of production of a box shaped container is $1 per box. - the current price for aluminum sheets of the required thickness is 0.65 cents per square centimeter. (Note this is less than one cent per square centimeter.) We need to advise the client on the dimensions of containers with lowest cost, considering cost of materials, production, and advantages and disadvantages of using cylindrical containers vs boxes. As an additional note, the cost of production of cylinders may rise. If you can address how that may affect the choice of shape, and at what production cost they should consider a change, there may be a bonus for you. Let me know by November 20. Mr Big