A rectangular storage container v an open top is to have a volume that 10 m3. The length of this base is double the width. Product for the base expenses \$15 every square meter. Product for the sides prices \$9 every square meter. Find the price of materials for the cheapest such container. (Round your answer to the nearest cent.) Suppose the broad is x (m), length of the basic is 2x (m), the base area is 2x^2 (m^2).

You are watching: A rectangular storage container with an open top is to have a volume of 10 m3

Since the volume is 10 (m^3), the height has to be 10/2x^2 (m) = 5/x^2.

The cost of making such container is

cost the base: 2x^2*15 = 30x^2

cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x

The in its entirety cost is thus the amount of the base and also the sides: f(x) = 30x^2 + 270/x

The gain the minimum,

df(x)/dx = 30*(2x - 9/x^2) = 0

so x = (9/2)^(1/3) = 1.651 (m)

f(x) = 245.31 (dollars)

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