Question

This assignment requires using the Excel add-in called Solver...

1. Can a linear programming problem have no solution? More than one solution? Explain.

2. To find the optimal solution to a linear optimization problem, do you have to examine all the points in the feasible region? Explain.

Answer 1

Linear Programming problem:

The problem given as optimize z=CX, subject to the constraints and non negativity restrictions.

For the LPP of two variables We can use Graphical method or simplex method.

Graphical method for solving LPP:

In the graphical method, we plot the equations by converting inequalities into equalities.

Then consider the feasible region of LPP.

1. No solution:

  When we do not have a feasible region then we have no solution.

Also, when the feasible region lie outside first quadrent then it have no solution.

e.g. a)

b)

2.More than one solution:

When we got two points having optimum solution, then we have more than one or infinite solution.

When two extreme points have optimum solution, the all the points lying on the line segment joining two extreme points are optimal points. Because there is convex combination.

e.g. maximize z=2x+5y; subject to  

3. Optimal solution

  To find optimal solution, without considering all the points in the feasible region, just considering the corner points or extreme points is sufficient.

Simplex Method

   For any number of variables simplex method is most efficient method.

In this we can directly obtain the solution.