Question

-/2 POINTS TANAPCALC10 8.5.001. Use the method of Lagrange multipliers to minimize the function subject to the given constraint. (Round your answers to three decimal places.) Minimize the function f(x, y) = x2 + 5y2 subject to the constraint x + y - 1 = 0. minimum of at (x, y) = 0 at (x, y) =( Need Help? Read It Watch It Talk to a Tutor

Answer 1

) 4 Giren function foc, y) = x²+542 le consternut guxiy xty-150 Let it be the lagrange multiplier. critical points occurs when [hr = dgx] & [fy = 19y) fa = (x²+542) = 2x to = 2x ty by (x2 +5y2 = ot 5(24) = loy & sn 9x = (x+y-1) = 1 +0 -0 = 1 y = 3 (SCty-1) = of 1-0 =1. (fx = Aga x=8 CD = 2d (1) fy=&gy 10y = ACD [x = loy (2) - 2x = 104 from constrant, altyal=0 sytylo 6y=1 9- - 0.1666 = 0·166 -- x - 5y = 8 x = 8) = 0.833 critical point occor at ( 3 ).) FC ) - 5) +500 +5=0833 minimum of (0.833 at (x,y) = ((0.833, 0.166)