Of all rectangles with area 324324, 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.

For w = 18 units perimeter is minimum

P = 2(18 + w)

Step-by-step explanation:

Given;

Area of the rectangle = 324 units²

P is the perimeter

w is the width

Let L be the length of the rectangle

therefore,

P = 2(L + w)  ............(1)

also,

Lw = 324

or

L = ..........(2)

substituting 2 in 1

P =

now,

for minimizing the perimeter

= 0

or

= 0

or

= 0

or

= -1

or

w² = 324

or

w = 18 units

For w = 18 units perimeter is minimum

therefore,

from 2

L =

or

L = 18 units

objective function for P is:

P = 2(18 + w)