A rectangular storage container with an open top is to have a volume of 10 m^3. The length of the...

Question:

A rectangular storage container with an open top is to have a volume of 10 {eq}m^3{/eq}. The length of the base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

Application of Differential Calculus: Optimization

According to Second Derivative Test, a function f(x) is said to have a minimum value at {eq}x = n {/eq} if {eq}f'(n) = 0 \text{ and } f''(n) >0. {/eq} The same function is said to have a maximum value at {eq}x = n {/eq} if {eq}f'(n) = 0 \text{ and } f''(n) <0. {/eq} We can use this concept to find the dimension of the box that will cost the cheapest.

Answer and Explanation:

The figure below shows an open top rectangular box.

Open top rectangular box

First, we need to determine the volume of the rectangular box. Note that the formula for...

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