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Mr. Fishman decides to build a rectangular pen for his pet llama. He will use the side of his house for one wall of the pen; therefore, he will not need any fencing on that side. On the other three sides, he will use special fencing that costs
$12
per foot. He wants the entire enclosed area to be 2400 square feet. Lastly, he needs four corner posts that cost
$5
each. a) [5 pts] Let
x
represent the length of the side of the pen perpendicular to the house and let
y
represent the length of the side pf the pen parallel to the house. Write a function
C(x)
for the cost of the materials for the Ilama pen in terms of
x
. Simplify your answer. Note: Diagram not to scale. b) [4 pts] Since the Cost Function is not quadratic, you will need to use your graphing calculator to determine the dimensions of the pasture that minimize cost. Set your viewing window on your calculator from
[0,150]
on the
x
-axis and
[0,5000]
on the
y
-axis and provide a labeled sketch of your graph. Then use the CALC capability on the calculator to find the minimum point. Round your answers for both the
x
and
y
dimensions to two decimal places and express your final answer using appropriate units. c) [3 pts] What is the minimum cost for Mr. Fishman to build this Ilama pen? Round your answer to the nearest cent and express your answer with appropriate units.

Sagot :

varshamittal029

a) The function C(x) for the cost of the materials for the pen in terms of x

is : c(x) = 24x+(28800/x)+20

b)  the dimensions of the pasture that minimize cost is:

x = 24.62 and y = 69.28

c) minimum cost for Mr. Fishman to build this Ilama pen is $1682.77

a) Perimeter of fence = 2x+y

∴ cost of fencing = 12(2x+y)

also cost of poses corner house = 4×5 = 20

∴ Total cost of pen = 24x+!2y+20

But area of the pen = 2400

xy = 2400

y = 2400/x

Putting 1 in total cost c(x)

= 24x+{(12×2400)/x}+20

c(x)= 24x+{28800/x}+20

b) we need to minimize c(x)

using the graphical calculator we obtain

That x = 34.61

x = 34.61 & y = 2400/34.61 = 69.28

c) Minimum value of c(x) = c(34×64) = boxed 1682.77

Minimum cost for Mr. Fishman to build this Ilama pen is $1682.77

Learn more about Minnimum value here:

brainly.com/question/2437551

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