Question

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

Answer 1

find the factors of 3750
find the perimeter

Answer 2

I'm confused

Answer 3

50 x 75 = 3750

Answer 4

ok

Answer 5

50 + 50 + 75 + 75 = Perimeter

Answer 6

ok

Answer 7

wait hold on i think i may have messed up lol

Answer 8

@electrokid can you see if i did this right?

Answer 9

@electrokid so far i have been able to do it 3 ways but each time i got a different answer

Answer 10

let the 2$ side be "l"
and 3$ side be w
\[A=l\times w=3750\\
C=2(2l)+3(2w)\\
C(w)=4\times{3750\over w}+6w
\]

Answer 11

now, maximize C(w)
so, its detrivative should be 0

Answer 12

\[C'(w)=-4\times{3750\over w^2}+6=0\\
6w^2=15000\\
w^2=2500\\
\boxed{w=50}\\
l={3750\over50}\implies\boxed{l=50}
\]

Answer 13

You know which dimension you are going to use the hi-dollar fence
the 50 ft, the 75 ft dimension will have the 2$ per ft. fencing.