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pantera1 [17]
4 years ago
5

Abc daycare wants to build a fence to enclose a rectangular playground. the area of the playground is 930 square feet. the fence

along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of brick, costs $20 per foot. find the length of the brick fence that will minimize the cost of enclosing the playground. (round your answer to one decimal place.)
Mathematics
1 answer:
Dahasolnce [82]4 years ago
4 0
Xy = 940 

<span>and </span>

<span>Cost = 5(2x) + 5y + 10y (I chose y to be the side with brick). The cost equation simplifies to: </span>

<span>C = 10x + 15y </span>

<span>Replace y in the cost equation with 940/x: </span>

<span>C = 10x + 15(940/x) </span>

<span>C = 10x + 14100/x <---this is the equation you need to minimize. </span>

<span>C' = 10 - 14100/x^2 </span>

<span>10 - 14100/x^2 = 0 </span>

<span>14100/x^2 = 10 </span>

<span>x^2 = 14100/10 = 1410 </span>

<span>x = sqrt(1410) = 37.55 </span>

<span>y = 25.03 <---this is the length of the brick fence.</span>
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First, we draw our line.

 

|------------------------------------------------------------------------------------|

a                                                                                                            e

 

 

Next, break up this line into segments using the information.

 

|----------------------|----------------------|--------------------|------------------|

a                            b                            c                         d                      e

 

 

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Due to midpoint theorem,

 

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The equations we will use are

 

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