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Mila [183]
4 years ago
15

A rectangular box is to have a square base and a volume of 20 ft3. if the material for the base costs $0.28 per square foot, the

material for the sides costs $0.10 per square foot, and the material for the top costs $0.22 per square foot, determine the dimensions of the box that can be constructed at minimum cost.
Mathematics
1 answer:
AleksandrR [38]4 years ago
7 0
Then the area of the top and bottom are each x^2. 
<span>Then the height of the box is 40/x^2. </span>
<span>Then each side of the box is 40/x square feet. </span>
<span>Then the area of all four sides is 160/x square feet. </span>
<span>Then the total cost is represented by: </span>
<span>0.30x^2 + 0.05 (160/x) + 0.20x^2 </span>
<span>Expand the middle term and combine x^2 terms: </span>
<span>0.50x^2 + 8/x </span>
<span>Rewrite for easy differentiation: </span>
<span>0.50x^2 + 8x^-1 </span>
<span>Take the derivative: </span>
<span>x - 8x^-2 </span>
<span>Set the derivative to zero: </span>
<span>x - (8/x^2) = 0 </span>
<span>Multiply by x^2 </span>
<span>x^3 - 8 = 0 </span>
<span>Add 8: </span>
<span>x^3 = 8 </span>
<span>Take the cube root: </span>
<span>x = 2 feet </span>
<span>So the height is 40/4 = 10 feet </span>
<span>So the dimensions with minimum cost are: </span>
<span>2 x 2 x 10 feet.</span>
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3 years ago
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MAXImum [283]

Answer:

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Step-by-step explanation:

<u><em>The question is </em></u>

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Part b) How old is Kevin?

Let

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we know that

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6 0
3 years ago
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3 years ago
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