Nicely done. The "Harvard Calculus" recommends tables, graphs, formulas, and words as problem-solving tools, and J can help with tables and graphs. About Roger's question, I am inclined to guess a half-ellipse for maximum area, but it's just a guess. --Kip
Sent from my iPad On Feb 23, 2013, at 11:37 AM, Raul Miller <rauldmil...@gmail.com> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
