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1 answer:
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Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be
Let h be the height of the box
V = Volume of the box =
Now surface area of the box with an open top is given
Differentiating with respect to x we get
Equating with zero
Double derivative of the function
So, x at 10.74 is the minimum value of the function.
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is
The area of the base is
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
The minimum cost of the box is 69.21 dollars.