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Math Help - minimum cost

  1. #1
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    minimum cost

    Greetings !

    A closed rectangular box with a square box with a square base and with a capacity of 1.5 meter cubed is to be made The material for the top and bottom costs $3.00 per meter squared and for the sides is $4.00 per meter squared. Find the minimum cost.

    I was able to get the 2 equations which are:

    (x^2)(height) = 1.5
    3x + 4h is a minimum

    dx/dh = 3x + 6/x^2

    then I equate this to zero

    which gave me x = 4 and height = 0.09375

    The cost of which is $12.375

    But this is not a correct solution.

    It is a multiple choice question, the selections are:

    a. $36.68 b. $45.86 c. $28.68 d. $43.98

    Any idea where I get wrong ?
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  2. #2
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    Quote Originally Posted by dugongster View Post
    Greetings !

    A closed rectangular box with a square box with a square base and with a capacity of 1.5 meter cubed is to be made The material for the top and bottom costs $3.00 per meter squared and for the sides is $4.00 per meter squared. Find the minimum cost.

    I was able to get the 2 equations which are:

    (x^2)(height) = 1.5
    3x + 4h is a minimum
    This is wrong. The cost of the bottom is $3 per square meter, not per meter. The area of the bottom is x^2 square meters. The area of each side, and there are 4 sides, is xh square meters.

    dx/dh = 3x + 6/x^2

    then I equate this to zero

    which gave me x = 4 and height = 0.09375

    The cost of which is $12.375

    But this is not a correct solution.

    It is a multiple choice question, the selections are:

    a. $36.68 b. $45.86 c. $28.68 d. $43.98

    Any idea where I get wrong ?
    I wonder why you thought "3x+ 4h" was the cost.
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  3. #3
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    Nov 2010
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    Aaah. Got 24/x + 6 x^2 is a minimum cost.

    Differentiated it. Giving me x = cube root of 2, and h = cube root of 4

    But still can't get a valid answer.
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