245.31 (dollars) is the cost (in dollars) of materials for the least expensive such container.
<h3>What is maxima and minima ? </h3>
Calculus maxima and minima are found using the concept of derivatives. Knowing that the derivative concept gives information about the slope/slope of a function, we find the point where the slope is zero. These points are called inflection points/stationary points. These are the points associated with the maximum or minimum (local) values of the function.
Knowledge of maxima and minima is essential for our everyday problems. In addition, this article also explains how to find the absolute maximum and minimum values.
Solvable maximum and minimum arithmetic problems are discussed in this article.
<h3>Calculation</h3>
Suppose the width is x (m), length of the base is 2x (m), the base area is 2x^2 (m^2).
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 of base: 2x^2*15 = 30x^2
cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x
The overall cost is hence the sum of the base and the sides: f(x) = 30x^2 + 270/x
The get 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)
learn more about maxima and minima here :
brainly.com/question/17467131
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