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Homework Statement
if you have dl/dx= -2 +0.002x-lagrange function(backword L)
dl/dy=0.012y-5-lagrange function
dl/dl= -(x+y-2000)
How do you solve for x, y and backword l?
nikk834 said:Homework Statement
if you have dl/dx= -2 +0.002x-lagrange function(backword L)
dl/dy=0.012y-5-lagrange function
dl/dl= -(x+y-2000)
How do you solve for x, y and backword l?
Homework Equations
The Attempt at a Solution
You can't solve that since, for one, it's not an equation. What does that expression equal? Once you have that sorted out, remember that you still have one more equation you can use to help you solve for x and y.nikk834 said:ok so lamda=2-0.02x
if i substitude that into the next equation i get 0.012y-5-2-0.02x
how do i solve for that when i got 2 variables x and y.
Lagrange's method, also known as the method of undetermined multipliers, is a mathematical technique used to find the maximum or minimum value of a function subject to a set of constraints. It is used in optimization problems where the objective function and constraints are defined by a set of equations.
The Lagrangian function is a mathematical function that combines the objective function and constraints into a single equation. It is used in Lagrange's method by introducing a set of multipliers, known as Lagrange multipliers, to the Lagrangian function to form a new function that can be optimized.
The steps to solve a problem using Lagrange's method are as follows:
1. Formulate the objective function and constraints as a set of equations.
2. Construct the Lagrangian function by combining the objective function and constraints.
3. Take the partial derivatives of the Lagrangian function with respect to each variable.
4. Set the derivatives equal to zero and solve for the variables.
5. Plug the values of the variables into the objective function to find the maximum or minimum value.
Lagrange's method can be used to solve problems with multiple variables and constraints, such as optimization problems in economics, physics, engineering, and other fields. It can also be applied to problems in calculus, such as finding the extreme values of a function.
Lagrange's method may not always provide a solution to a problem, especially when the objective function and constraints are highly nonlinear or when there are many variables and constraints involved. It also requires the existence of continuous partial derivatives of the objective function and constraints, which may not always be the case.