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Homework Help: Integrating a square box to find maximum volume

  1. May 31, 2012 #1
    Hi guys!
    I thought it was [STRIKE]intergration[/STRIKE]integration, i think its differentiation.

    Im having problems trying to figure out where to start with this question:

    A rectangular tank with a square base x meters and height h meters is to be made from two different materials.

    Material for the sides and top cost $65 per square meter, the material for the base cost $130 per square meter and the total cost is $5,000.

    a) Show that the volume of the tank can be give by V= x²(5000-195x²/260x).

    b) Determine the dimensions of the tank for maximum volume.

    Now, from what I gather V= b X l X h or b²Xh. All valves seem to be a factor of $65 ie the darer material is twice the price of the cheaper material.

    I just need someone to help me understand what I should be looking for, the square meter part throws me off.

    Any help will be much appreciated,

    Last edited by a moderator: May 31, 2012
  2. jcsd
  3. May 31, 2012 #2


    Staff: Mentor

    What you wrote is V = x2[5000 - (195x2/260x)]. Is that what you are asked to show? If it isn't, then you need some more parentheses.
    Don't use X to indicate multiplication, especially when x is already a variable in the problem. You can write this as V = b2h or b2 * h.

    Why are you using b, though? In the problem statement, it says that the base of the tank is a square that is x meters on each side, so V = x2h.
    There is a limitation of $5000 for materials. Draw a picture of a box with a top, and write expressions for the areas of the bottom, top, and four sides.

    Then write an expression for the total cost, given that the bottom needs to be made of the more expensive stuff, and the sides and top made of the cheaper stuff.
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