You are building 5 identical pens next to each other. What dimensions minimize the amount of fencing if you want each area small area to be 375 square feet

Question

You are building 5 identical pens next to each other. What dimensions minimize the amount of fencing if you want each area small area to be 375 square feet.

Any help would be amazing

Answer 1

Darrel, I drew a sketch with 5 rectangles, connected to each other, and I have 10 "x" lengths and 6 "y" lengths for my shape--does this fit the problem?

We then see if each pen is 375 in area, that (x)(y) = 375, so y = 375/x

Now we can look at the perimeter of this (how many "x" and "y" lengths we need) and see we have

P(x) = 10x + 6y or P(x) = 10x + 6(375/x)

To find the minimum value, find where P'(x) = 0 and P"(x) < 0

Hope this helps, but please let me know---Andrew

Answer 2

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