A farmer is building a rectangular, three-sided fence next to a river. One of the sides is $15/foot while the other two are $10/foot. The area must be 1.6 million square feet. Find the dimensions that minimize the cost of the fence.

Question

A farmer is building a rectangular, three-sided fence next to a river.  One of the sides is $15/foot while the other two are $10/foot.  The area must be 1.6 million square feet. Find the dimensions that minimize the cost of the fence.

anonymous · Answer

$$C=10x+15y+15y =10x+30y  $$

use A=xy=1.6 to solve for y in terms of x then substitute into the cost function , take the derivative and find the critital points the minimal will occur at the critical point

anonymous · Answer

I plug the critical points back into the Cost of Area equation
?

anonymous · Answer

*cost or area

anonymous · Answer

$$y=1,600,000/x$$ substitute this into the cost function for y. then take the derivative of the cost function

anonymous · Answer

sorry the cost function is $$C=20x +15y$$

anonymous · Answer

So you end up with C = 20(1,600,000/y) + 15y

anonymous · Answer

which is C = 32,000,000/y + 15y

anonymous · Answer

WOULD THE area be A=xy or A=2xy