Question

(a) Solve the following problem using Lagrange's method [ max x y text { subject to } p x+q y=m ]

(b) The optimal choices and ( y of ( x ) and ( y ) both depend on ( p

Answer 1

To solve using Lagrange's method, identify the objective function and the constraint equation. Write the Lagrangian function, differentiate it, and solve the resulting system of equations.

Step-by-step explanation:

To solve the given problem using Lagrange's method, follow these steps:

1. Identify the objective function and the constraint equation.
2. Write the Lagrangian function using the objective function, constraint equation, and Lagrange multiplier.
3. Differentiate the Lagrangian function with respect to both variables (x and y) and the Lagrange multiplier.
4. Set the derivatives equal to zero and solve the resulting system of equations.
5. Substitute the values of x and y into the constraint equation to find the optimal choices.