I have this lagrangian function question.
U(x,y)= ln(x) + 0.04ln(y), given the constraint x+(y/1.08)=20
set the lagragian as L(x,y,λ)=ln(x) + 0.04ln y) - λ(x+(y/1.08)-20)
got dL/dx = 1/x - λ = 0 --> x = 1/λ
dL/dy = 0.04/y - λ/1.08 =0 --> 0.04/y = λ/1.08 --> y = (0.04*1.08)/λ --> y = 0.0432/λ
substituted these values into dL/dλ = 20-x-(y/1.08), and got λ=0.05216.
however, i double checked my answer on wolfram alpha and λ should equal 250/13. i cannot see where i went wrong, somebody help pls.
U(x,y)= ln(x) + 0.04ln(y), given the constraint x+(y/1.08)=20
set the lagragian as L(x,y,λ)=ln(x) + 0.04ln y) - λ(x+(y/1.08)-20)
got dL/dx = 1/x - λ = 0 --> x = 1/λ
dL/dy = 0.04/y - λ/1.08 =0 --> 0.04/y = λ/1.08 --> y = (0.04*1.08)/λ --> y = 0.0432/λ
substituted these values into dL/dλ = 20-x-(y/1.08), and got λ=0.05216.
however, i double checked my answer on wolfram alpha and λ should equal 250/13. i cannot see where i went wrong, somebody help pls.