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** Using Calculus** We have a client asking for our recommendations on which storage containers are better...

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Basic Math

** Using Calculus**

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

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