Question

Determine the extrema of gew v= bu- Subject to the constraint Kity's 360

Answer 1

2 According to questron, function goven gruan) = bu .bt subject to constant 22tog? = 360 Both the functron and the constant are two ameneron and 14,t) is dummy waterable so we can replace to gomy) then apply dangranges multipliers. 4 cm, y) = grn, y) tÅ Gal²ty 2-360) ba +7 ( 12 ty? -360) Bifferentrate wrat a and then yt equate to o suppose 2 by a Ha a b + X(2n) => 2 21 b Hy b +Xlay) 20 2 4 y we can write as both equal to è he al à 810 ЧЧ 27 44 - 1 27 4 y -an 27 y 2 er 2x (y །ད -29

لأولى n² + y2 = 360 n of rom equation all 2 + *2=360 5 CA ) H, 20 we put in for yand above equatron 72 =360 - Ea2=360 4 = n² = 36084 ob 288 27 na 4/288 11282 1282,-122 Now put the value of a incal we get the value of y y2 +288 = 360 27 y2=72 27 y 24652 so the extrema points of a subject to constramts s?tyr =360 are (1252,682), (1282,-652), (=1282,662), (-1252,-682) so these points are extrema, In these point the functim atdarns marmum or monomum. As it alld not ask to find maxma or monima, & stopped stopped hear hear by finding entrema,