Question

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

Answer 1

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:

$I)width$

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