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# Lagrange Multiplier Calculator

To use lagrange multiplier calculator, enter the values in the given boxes, select to maximize or minimize, and click the **calcualte** button

## Lagrange Calculator

Lagrange multiplier calculator is used to evaluate the maxima and minima of the function with steps. This Lagrange calculator finds the result in a couple of a second.

## What is the Lagrange multiplier?

The method of **Lagrange multipliers**, which is named after the mathematician `Joseph-Louis Lagrange`

, is a technique for locating the local **maxima **and **minima **of a function that is subject to equality constraints.

(i.e., subject to the requirement that one or more **equations **have to be precisely satisfied by the chosen **values **of the **variables**).

The fundamental concept is to transform a limited problem into a format that still allows the derivative test of an unconstrained problem to be used.

The **Lagrangian function** is a reformulation of the original issue that results from the relationship between the gradient of the **function **and the gradients of the **constraints**.

## The formula for the Lagrange multiplier

The `formula of the Lagrange multiplier`

is:

**Example of Lagrange multiplier**

Use the method of Lagrange multipliers to find the minimum value of **g(y, t) = y ^{2} + 4t^{2} – 2y + 8t** subjected to constraint

**y + 2t = 7**

**Solution:**

**Step 1: **Write the objective function and find the constraint function; we must first make the right-hand side equal to zero.

g(y, t) = y^{2} + 4t^{2} – 2y + 8t

The constraint function is `y + 2t – 7 = 0`

So** h(y, t) = y + 2t – 7**

To minimize the value of function **g(y, t)**, under the given constraints.

`g(y, t) = y`

corresponding to ^{2} + 4t^{2} – 2y + 8t**c = 10** and **26**.

**Step 2: **Now find the gradients of both functions.

∇g(y, t) = (2y - 2)**i** + (8t + 8)**j**

∇h(y, t) = **i** + 2**j**

Now equation **∇g(y, t) = a∇h(y, t)** becomes

(2y-2)**i** + (8t + 8)**j **= a(i + 2j)

**Step 3:** Compare the above equation.

2y - 2 = a

8t + 8 = 2a

**Step 4: **Now solve the system of the linear equation.

t= 1 and y= 5

**Step 5: **Evaluate the function

g(y, t) = 5^{2}+ 4(1)^{2} – 2(5) + 8(1) = 27

So **h** has a relative minimum value is **27** at the point **(5,1)**.

Use our ` Lagrangian calculator `

above to cross-check the above result.