## Constraint Minimization-Pen and Paper Calculation

f(x) = 5-(x-2)^2 - 2(y-1)^2

5 - x^2-4+4x-2y^2-2+4y = 0

-x^2-2y^2+4x+4y-1=0

g(x)=f(x)+λ

g(x) = -x^2-2y^2+4x+4y-1 + λ (x+4y-3)

(del g)/(del x) = -2x+4+λ = 0  -----eq 1

(del g)/(dely) = -4y+4+4λ= 0 ------  eq2

(del g)/(del λ) = x +4y-3 =0 -----    eq3

-4y+4+4λ = 0 ---   eq2

/4 in common

-y+1+λ = 0

λ = y-1----- eq 4

putting eq4  in eq 1 and 3

-2x + y + 3 = 0------eq5

2x + 8y -6 = 0  ------eq6

eq5/eq6

-2x + y +3 = 0

2x + 8y - 6 = 0

-------------------

9y - 3 = 0

y = 1/3

λ = (1/3)-1

λ = -2/3

-2x + y + 3 = 0

-2x + (1/3) =3 =0

x =5/3

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