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#?
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
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
Their stationary points are determined by solving
so we obtain