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You are an engineer in charge of designing the dimensions of a box-like building. The base is rectangular in shape with width being twice as large as length. (Therefore so is the ceiling.) The volume is to be 1944000 m3. Local bylaws stipulate that the building must be no higher than 30 m. Suppose the walls cost twice as much per m2 as the ceiling, and suppose the floor (i.e.base) costs nothing. Find the dimensions of the building that would minimize the cost.

  • Calculus -

    The answer might be easy if you told us the minimum height requirement.

    Since the ceiling is cheaper, the lower the height, the cheaper it will be.

    Once we know that, the squarer the building, As equal as possible in length & width, the smaller the perimeter and therefore the less m2 of walls.

    Hope this helps

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