Question

** Using Calculus**

We have a client asking for our recommendations on which storage containers are better for shipping and storing hazardous waste. Their requirements are as follows: The container should hold 50,000 cm3 (which is 50 liters); The sides of the container will be made from aluminum sheets with a thickness of 2 mm; The two bases of the container need to be thicker (for greater support) and will be made from aluminum sheets with a thickness of 6 mm; There are two options to consider for the shape of the containers: Option 1: closed cylinders; Option 2: closed boxes with a square base (note the top and bottom are squares, but the sides could be rectangles). Some considerations to take into account: The fixed cost of production of a cylinder container is $10 per cylinder; The fixed cost of production of a box container is $4 per box; The current price for 2mm aluminum sheets is $0.011 per square centimeter. The current price for 6mm aluminum sheets is $0.045 per square centimeter; You need to advise the client on the dimensions of the containers that will both meet the size requirement and minimize cost. Based on the cost, you should make a recommendation to the client on whether square or cylinder containers should be used.

Answer 1