Question

Question 23 Find the maximum of f(x, y) = 5x 3y subject to the constraint x? + y =136. 80 54 68 72 None of the above or below 136

Answer 1

Given freign = 5x-3y st x ry? 136. gery) = xy = 136 50 Now faca.y)=5 Jx (2,91= 2x Jy (39) = gy the relation as Now we have 3 g putting this Nalue in we have x25 » fyin, y2 = -3 using facm, 9 ) Agu 29) f fyen, 9) =18, 04,99 5 = + (2x) f -2=4224) > d= (5/2x) and x=-Blays (7/2) = -(3/3) geny) x + 2 - 1 2 1 2 = 126 + 8 + 2 x ² = 136 st?lit af) = 136 * 12( 34) -136 & 2² = 68 4825=100 then and At n=-10 y=-(3)(10) = -6 y = - ( 7 ) (-10) = 6 point of mapima f minima are (19) ='(10,-6) and (-10,6) The value of f(x,y) at- (10,-6) is $110,-6)= 15 (18)-3(-6) = 50+ 18 = 68 and al- (-10,6) is ft-10,6)= 51-10) - 316) = -50-18 --60 Hence the maximum value of finy) is at (10,-6) and is finy) = 60 option © in correct. [x = 110 At n=10 Hence the