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March 29, 2017

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A cylindrical container with a volume of 3000 cm^3 is constructed from two types of material. The side and bottom of the container cost $0.10/cm^2 and the top of the container costs $0.20/cm^2.

a) Determine the radius and height that will minimize the cost.

b) Determine the ratio of diameter to height.

Could you please help me with these questions please and thank you

  • Calculus - Optimization - ,

    Cost=.10*(pi*r^2+2Pi*r*h)+.20PIr^2

    volume= PIr^2h or h= volume/PIr^2
    h=3000/(PIr^2)

    Put that into the cost function for h.

    Then take the derivative of cost with respect to r (dCost/dr), set equal to zero, solve for r.

  • Calculus - Optimization - ,

    lol i need help on the same one

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