Arectangular 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 $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.) $

$ 327.08

Step-by-step explanation:

Let w be the width ( in meters ) of the container,

⇒ Length of the container = 2w,

If h be the height of the container,

So, the volume of the container = length × width × height

= 2w × w × h

= 2w² h

According to the question,

Now, the area of the base = length × width

Area of sides = 2 × length × height + 2 × width × height

Since, material for the base costs $20 per square meter and material for the sides costs $12 per square meter,

Hence, total cost,

Differentiating with respect to w,

Again differentiating with respect to w,

For maxima or minima,

C'(w) = 0

For w = 1.651, C''(w) = positive,

Thus, cost is minimum for width 1.651 meters,

And, the minimum cost = C(1.651) =

123

step-by-step explanation:

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