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Delicious77 [7]
3 years ago
8

if all rectangles with area 4​, which one has the minimum​ perimeter?Let P and w be the perimeter and​ width, respectively, of t

he rectangle. Write the objective function in terms of P and w. Assume that the width is less than the length if the dimensions are unequal.
Social Studies
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

1) A rectangle whose width measures 1 and length 4. 2) Objective function: in terms of P and w

\frac{2w^{2}+16}{w}=P

Explanation:

1) Consider that the rectangle dimensions are made up of Integer numbers greater than 0, assuming w < l, and the product of w times l must be equal to 4. A rectangle whose width measures 1 and length 4

Then it comes:

I)width

\\Objective \: function: in \,  terms\, of \, P\, and\, w:\\2w+4l=P\\ w*l=4\\l=\frac{4}{w}\: \\2w+4\frac{4}{w}=P\:\\ \: 2w+\frac{16}{w}=P\\\: \: \frac{2w^{2}+16}{w}=P

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