Question

I have no idea where to start for this optimization problem

1. A farmer with 800ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

Answer 1

ar As shown in - di fig let a& y y be dimensions of each pen. - z Total length of fencing required = 4x+42454 = 8x45y ii 84+5y = fuo ft ya < (500-8a) та ер бала - - 4* - «ч ACH) -- 47. (1800-8) et (roon-8a) Aca) – 32 (1009-a) Alca) = 32(100-23) Alcal=0 for maximum calea =) 32(100-20) = 0 =) 100-29 20

- 20=100 n=50 SA"(a) = }} (-2) =-64 < area a 1. =) we get maximum - Maximum area T ACSO) = 32 (100kso -50%) = 72 x (106-50) = 160000 ft Mae area = 16000 sq.ft