# How do you find the maximum and minimum values of the function subject to the given constraints: #x+y>=2, 7x-y<=14, 3y<=5x+6, f(x,y)=4x+7y#?

##### 1 Answer

See below.

#### Explanation:

How do you find the maximum and minimum values of the function subject to the given constraints:

This is a typical linear programming problem. It can be assembled as

Here

This example was worked out with the Lagrange Multipliers technique. The attached plot shows the feasible region with the main points shown at the frontier. The black vectors show the gradient direction at the stationary points and the red vectors show the restrictions gradient at those points. The maximum point is located at

So defining

Now calling

Their stationary points are determined by solving

for

so we obtain