##### determine the dimensions of the enclosure that can be erected at minimum cost

 Calculus Tutor: None Selected Time limit: 1 Day

Jul 17th, 2015

Let one side of the fencing be x ft and the other side be y ft

2) So, x*y = 912; ==> y = 912/x

3) The three sides fencing can be either (2 sides with x and one side with y) or (2 sides with y and one side with x)

4) This implies, the fencing length of 3 sides is either (2x + y) or (x + 2y); so there could be four types cost modelling taking into account of the variation in cost of different fencing:

So let us work on each model:

i) (x, y) = (\$2, \$6) & P = 2x + y

==> C = 4x + 6y; substituting for y from (2), C = 4x + (6*912)/x
Differentiating C' = 4 - (6*912)/x^2;
equating this to zero and solving, x = 36.986 ft (nearly)
Again differentiating, C'' = (12*912)/x^3, which is > 0 for x = 36.986;
Hence cost is least.

Roughly taking x = 37 ft, the cost in this case will be nearly \$296.

ii) (x, y) = (\$6, \$2) & P = 2x + y

==> C = 12x + 2y = 12x + 1824/x;
==> C' = 12 - 1824/x^2; setting to zero and solving, x = 12.329 ft
Here also C'' at x = 12.329 will be > 0, hence it is least

Roughly taking x = 12.3 ft, the cost in this case also will be nearly \$296.

iii) (x, y) = (\$2, \$6) & P = x + 2y

Proceeding in similar lines as above, x = 73.97 ft and
cost in this case also is nearly \$296.

iv) (x, y) = (\$6, \$2) & P = x + 2y

Proceeding in similar lines as above, x = 24.66 ft and cost
in this case also is nearly \$296.

As such in any choice, the cost of fencing remain same; so according to the availability of materials and design any one of the four design can be selected.

However I feel selecting 37 ft on two sides with steel fencing and one side of about 24.6 ft with pine board fencing may be better for appearance.

Jul 17th, 2015

i dont understand what the answer is

Jul 17th, 2015

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Jul 17th, 2015
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Jul 17th, 2015
May 24th, 2017
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