Design a rectangular dog pen that has the greatest possible area and keep within a budget of $50. Your pen needs at least one gate for your dog. Fencing is $1.00 per foot, fence posts are $2.00 each, and gates(3 feet wide) are $5.00 each. What is the area of a pen?

Question

pls help me!!!

Answer 1

If the pen has dimensions x and y, with n gates, and assuming there are posts only at the corners and on both sides of the gate(s) and that the gate(s) do not share a corner post, then using up the whole budget,

(2x+2y-3n)+2(4+2n)+5n = 50
x+y+3n = 25
and, since the gates are 3' wide,
x > 3
y > 3

More gates mean less budget for fence, so go with one gate

That gives x+y=22 and since the maximum area for a given perimeter is a square, the dog pen will be

11 by 11, with one gate.

Cost for 39 feet of fence, one gate, and 6 posts is 39+5+12=50

Answer 2

thsnku so much steve!!

Answer 3

Pls still I don't understand how u got 25 could u pls tell me than tell me what is the area of the rectangle dog pen?
Pls help me

Answer 4

Above 39+5+12=56.

Correct size is 9x9.
9+9+9+6=33ft fence= $33
6 posts = $12
1 gate = $ 5
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$50