Astorage box with a square base must have a volume of 90 cubic centimeters. the top and bottom cost $0.60 per square centimeter and the sides cost $0.30 per square centimeter. find the dimensions that will minimize cost. (let x represent the length of the sides of the square base and let y represent the height.

Answer-

For side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

Solution-

Let us assume that,

x represents the length of the sides of the square base,

y represent the height.

Given the volume of the box is 90 cm³, so

As the top and bottom cost $0.60 per cm² and the sides cost $0.30 per cm². Total cost C will be,

Then,

As C'' has all positive terms  so, for every positive value of x (as length can't be negative), C'' is positive.

So, for minima C' = 0

Then,

Therefore, for side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

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