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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