Question

A rectangular area of 3750 square feet is to be fenced off. Two opposite sides will have fencing that costs $2 per foot and the remaining sides will ise fencing that costs $3 per foot. Find the dimensions of the rectangle that will minimize the cost.

Answer 1

\(C=2x+2x+3y+3y=4x+6y\) and \(xy=3750\) so \(y=\frac{3750}{x}\) and now
\[C(x)=4x+6\times \frac{3750}{x}\]

Answer 2

minimize that by taking the derivative and finding the critical points for \(x>0\)

Answer 3

critical points would be 4

Answer 4

total answer for 5641

Answer 5

seems unlikely

Answer 6

what did I do wrong

Answer 7

\[C(x)=4x+\frac{22500}{x}\]
\[C'(x)=4-\frac{22500}{x^2}\] set this equal to zero and solve

Answer 8

\[4-\frac{22500}{x^2}=0\]
\[\frac{22500}{x^2}=4\]
\[4x^2=22500\]
etc

Answer 9

i think you get \(x=75\)

Answer 10

ok I get 75 and -75

Answer 11

forget the negative one

Answer 12

ok so then 75 is that it

Answer 13

is that all that I need