Question

you have $4000 with which to build a rectangular enclosure with fencing. the fencing material costs $30 per meter. you also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. the material for the partitions costs $25 per meter. what is the maximum area you can achieve for the enclosure? (round your answer to the nearest whole number.) incorrect: your answer is incorrect. m2

Answer 1

The enclosure can be as large as 606 m2 in total.

Given that,

Let x be length of y be width of enclosure

fencing material cost $ 30 / m

Partition material cost $25/m

Total cost = (x+x+y+y)x 30+(y + y) x 25

c= 60(x+y) + 50y = 60 x + 110 y

4000 = 60 x + 110y

y = ( 400 - 6x / 11)

Now,Area of enclosure = x*y

A = x*(400 - 6x / 11)

A'(x)= 400-12x/11

for maximum area A'(x) = 0

400 - 12x/11 = 0,12x = 400,x = 100/3

A " ( x) = - 12/11 < 0  i.e., maximum

y = 400 - 6( 400/12 ) = 200/11 m

Maximum area = xy = 100/3 * 200/11 = 20000/33

                                                            =606.0606

A max = 606m²

Hence, the maximum area you can achieve for the enclosure is 606m²

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