Question

1. Solve using Lagrange multipliers: A farmer plans to fence a rectangular field that is bordered on one side by a stream. He can pay for 800 meters of fence Find the dimensions of the field that maximize the area. 2. Find the point on the planer + 2y + 32 = 13 closest to the point (1,1,1)

Answer 1

det length of sectangular field bex then gel+62 800 -Oltencing length - Le, Se, y) : 8x+4-Wo o Area = axy - flogy) = xy By lagrange multiplier fatdea 20 & fytddy zo - 4 +421_20 - 2 + d (U20 - 42-21 X2-1 tsomo --21-2d 2800 2800 ď 2 -200 az 200 2400 - 42200 &y=400 manimize the area. CScanned with damScanner

Q2 let 44,2) be point on plane {x+2y + 32 ² 136 closest to point ? nimel l __ then Die Ju-1)²+(4+1)+(2-02 det flamy 2 (219+(4-02+2th Blay) z U+ 24 +32 -13_ tot doneo 212-1 + 2D 2212 fut day so = 2141) tgd 20 y ²1-1 Ł edo z 202 2(24)+ 30 s072 21-3 A from 1 + $41=2) +36 1=3) =1 sur + 9 -88 +3 -94 B - 70 27 X 28 yo 2.22 0 1 (3, 2, is a point on ntly + 32= 13 | - closest to point (1,1,1) ned-with-GamSeanner