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.

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:

[tex]I)width<length \\II)w*l=4\\A=1*4\\P=w+w+l+l\therefore P=2(w+l)\\P=2(1+4)\\P=2(5)\\P=10\\A=w*l\; \therefore A=1*4\therefore A=4\\Objective \: function:\\2w+4l=P\\[/tex]

[tex]\\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[/tex]

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.

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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.