Hi J'ers The communication below was sent to, but seemingly not received by, <programm...@jsoftware.com>. So I resend itfor your information. - Bo
>________________________________ > Fra: Bo Jacoby <bojac...@yahoo.dk> >Til: "programm...@jsoftware.com" <programm...@jsoftware.com> >Sendt: 20:05 søndag den 24. februar 2013 >Emne: SV: [Jprogramming] The farmer's fence > > >Among the many answers in this thread about the farmer's fence the standard >method is not seen, so here it comes. > > >Let the sides of the rectangular chicken yard be x and y >The area is x*yDifferentiating the area gives 0=(y*dx)+(x*dy) which is zero >because the area is maximum. >The length of fence is 100= (2*x)+y >Differentiating the length gives 0=(2*dx)+(dy) which is zero because the >lenght is constant. > >Multiplying 0=(2*dx)+(dy) by x (called a Lagrange multiplyer) gives >0=(2*x*dx)+(x*dy) > >Subtracting 0=(2*x*dx)+(x*dy) from 0=(y*dx)+(x*dy) gives 0=(y-2*x)*dx >As dx need not be zero we must have 0=y-2*x . > >The rest is easy. > >So y=2*x . > >Substitute y=2*x into 100=(2*x)+y and get 100=4*x. > >Divide by 4 and get x=25 > >Substitute x=25 into 100=(2*x)+y and get y=50. > > > >No computer power is required. >- Bo > > >>________________________________ >> Fra: km <k...@math.uh.edu> >>Til: programm...@jsoftware.com >>Sendt: 15:42 lørdag den 23. februar 2013 >>Emne: [Jprogramming] The farmer's fence >> >>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
