As a first pass, let's consider integer valued lengths for the lengths of one of the fences. For simplicity, let's include cases where the area is zero. L1=: i.101
Since I allowed this fence to be 100 meters in length, that means that the other two sides are equal length and use the remainder of the fencing: L2=: -: 100-L1 And, since this is a rectangular fence, the areas are: A=: L1*L2 The largest area found so far is, thus: >./,A 1250 This corresponds to: (1250=A)#L1,.L2 50 25 One side is 50 meters, and the other sides are half that. Plotting these values, we see that 50 meters corresponds to the apex of a parabola, and there's no need to consider further where the maxima is at. FYI, -- Raul On Sat, Feb 23, 2013 at 9:42 AM, km <k...@math.uh.edu> wrote: > Use J to solve the farmer's fence problem: > > A farmer with 100 meters of wire fence wants to make a rectangular chicken > yard using an existing barn wall for one of the north-south sides. What is > the largest area he can enclose if he uses the 100 meters of fence for the > other three sides, and what are the dimensions of the largest-area chicken > yard? > > Kip Murray > > Sent from my iPad > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
