1. Home
  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization constrained extremum problems
  5. Method of Lagrange
  6. Exercise 2

Exercise 2

A constrained extremum problem with restriction $x+4y=8$ has as solution $z(1,2)=12$. The shadow price is $\lambda=-3$. Approximate the value of the minimum if we change the restriction into $x+4y=7$.
15
9
13
11
A constrained extremum problem with restriction $x+4y=8$ has as solution $z(1,2)=12$. The shadow price is $\lambda=-3$. Approximate the value of the minimum if we change the restriction into $x+4y=7$.
Antwoord 1 correct
Correct
Antwoord 2 optie
9
Antwoord 2 correct
Fout
Antwoord 3 optie
13
Antwoord 3 correct
Fout
Antwoord 4 optie
11
Antwoord 4 correct
Fout
Antwoord 1 optie
15
Antwoord 1 feedback
Correct: The shadow price is negative. Hence, if the constant in the constraint is lowered, then the value of the minimum increases: $12-(-3)=15$.

Go on.
Antwoord 2 feedback
Wrong: The shadow price is negative.

Try again.
Antwoord 3 feedback
Wrong: The shadow price indicates by much the value of the minimum changes approximately if the constant in the restriction increases by one.

See
Antwoord 4 feedback
Wrong: The shadow price indicates by much the value of the minimum changes approximately if the constant in the restriction increases by one.

See