Question

A rectangular area of 3200 ft2 is to be fenced off. Two opposite sides will use
fencing costing $1 per foot and the remaining sides will use fencing costing $2
per foot. Find the dimensions of the rectangle of least cost?

Answer 1

please provide me full answer , solution till end. thanks in advance

Answer 2

I assume this is a calculus problem. Let the dimensions be x by y, so\[xy=3200 \implies y= \frac{3200}{x}\]and\[C(x,y)=x+2y~or~C(x)=x+\frac{6400}{x}\]Differentiate C(x) and set the derivative to zero. That will give you a critical value for x. From that you can confirm that it is a minimum, and solve for y.

Answer 3

yes it is in calculas, will you do diffrerntiaite in it also?

Answer 4

It looks like \[C'(x)=1-\frac{6400}{x^2}=0 \implies x=80 \implies y=40\]So the enclosure is 80 feet long on the sides with the cheaper fence, and 40 feet long on the sides with the more expensive fence.

Answer 5

thanks

Answer 6

No sweat. Do math every day.