Question

Solve the optimization problem.
Minimize F = x2 + y2 with x + 2y = 5.
F= ?

Answer 1

\[F=(5-2y)^2+y^2\]
\[F(y)=25-20y+5y^2\]

Answer 2

\[F^'(y)=10y-20=0\]
\[y=2\]
\[x=5-2(2)=1\]
\[F(1,2)=1^2+2^2=5\]

Answer 3

Thanks for the help!!