What dementions will use the smallest amount of fencing?

A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enought grass for the herd, the pasture must contain 180,000 sqaure meters. No fencing is required along the river.|||Let length opposite river be L.


Let the ends be width W.


L*W = 180,000


L = 180,000/W





Total amount needed T = 2W + L


T = 2W + 180000/W





Differentiate to find dT/dW and equate to zero.


Solve the equation to find the value of W that minimises total.


From this find L and then T from formulas above.





You should find that W, L and T are all different multiples of 100.|||Okay, let x be length, y be width, then xy=180,000, or x=180,000/y and


the length of fencing is 2x+y.


So substitute the length is ((2*180,000)/y)+y.


So, differinate and set to 0,


so, -((2*180,000)/y^2)+1=0, so


y=squareroot(2*180,000).


And x=180,000/(sqr(2*180,000)).





And 2nd derviative test yields


((2*2*180000)/y^3 which if you plug in y is %26gt;0, which means it is the minimum.