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    ashley123456789's Avatar
    ashley123456789 Posts: 2, Reputation: 1
    New Member

    Jan 4, 2007, 06:56 PM
    Precalculus - OPTIMIZATION
    A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member

    Jan 5, 2007, 11:08 AM
    The surface area of a cylinder(with top and bottom) is given by:

    ... [1]

    Volume is: ... [2]

    Remember your costs:

    Using [1], the cost of the material would then be:

    ... [3]

    Now, solve [2] for h and sub into [3]. You will then have the function in terms of r alone.

    Differentiate, set to 0 and solve for r. Once you have r, h will follow.

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