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?
pls help me!!!
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
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
thsnku so much steve!!
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
To design a rectangular dog pen with the greatest possible area within a budget of $50, we need to consider the cost of the fencing, fence posts, and gates. Let's break down the steps to find the maximum area while staying within the budget:
1. Determine the cost constraints:
- Fencing: $1.00 per foot.
- Fence posts: $2.00 each.
- Gates: $5.00 each.
- Budget: $50.00.
2. Determine the dimensions of the rectangular pen:
- Let's assume the length of the pen is longer than its width to maximize the area.
- Let's consider the length of the pen as 'L' and the width as 'W'.
3. Calculate the cost of fencing:
- The cost of one side of the length will be 'L' multiplied by the cost of fencing per foot ($1.00).
- The cost of one side of the width will be 'W' multiplied by the cost of fencing per foot ($1.00).
- Since there are two sides of the length and two sides of the width, the total cost of fencing will be: (2L + 2W) * $1.00.
4. Calculate the cost of fence posts:
- The total number of fence posts required will be the sum of the number of posts for the length and the width.
- The number of posts for the length will be 2 (since there are two vertical sides), and the number of posts for the width will be 2.
- The total cost of fence posts will be: (2 + 2) * $2.00.
5. Calculate the cost of the gate(s):
- Since we need at least one gate, the cost will be $5.00.
6. Set up the cost equation and solve for the dimensions:
- The total cost of the pen should be within the budget of $50.00.
- The equation will be: (2L + 2W) * $1.00 + (2 + 2) * $2.00 + $5.00 <= $50.00.
7. Simplify the equation:
- 2L + 2W + 4 + 5 <= 50
- 2L + 2W <= 41
- L + W <= 20.5
8. Determine the maximum possible area:
- The area of the rectangular pen is given by A = L * W.
- To maximize the area, we need to find the maximum possible values for L and W while satisfying the equation L + W <= 20.5.
- Let's take the scenario where L = 10.5 and W = 10.0 (keeping in mind that L needs to be longer than W since it was assumed earlier).
- The area will be: A = 10.5 * 10.0 = 105 square feet.
Therefore, the maximum possible area for the dog pen under the given budget and constraints is 105 square feet.