Storage Container

Find the cost of materials for a rectangular storage container with an open top and V=10 m^3.?

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

haha. webassign is so fun. basically you’re trying to find the local minimum of the curve (which is when the derivative is equal to zero. So:

you trying to minimize area, and the formula for that is 2w^2 + the area of the sides which is solved here:

You first put 10=2w^2*h and solve for (h) which gives you 5/w^2. that means the area for the sides are 2 formulas (rectangle has diff. sides) which are:
Length x Height = 2w * 5/w^2 = 10/w
width x height = w * 5/x^2 = 5/w

next you need to add the costs in to make the formula for the costs of the area and not just the area so:

Cost = $10(2w^2)+$6(2*10/x)+$6(5/w)
cost = 20w^2+108/w

now you have you’re cost formula. and to find the minimum cost, you take the derivative:

derivative of cost = (20(2w^3-9))/w^2

find what zeros it out (which is the cubed root of 4.5. something like 1.65. then you plug that into the cost formula and you get $163.54.

Hope this helps!

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