# Calculus - Optimization

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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.

• 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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