Linear Programming Calculator is an online tool which makes calculations easy and fast. Try our free Linear Programming Calculator and understand the various steps.

Linear Programming Calculator is an online tool which makes calculations easy and fast. Try our free Linear Programming Calculator and understand the various steps.

PHPSimplex is an online tool for solving linear programming problems. Usage is free. To access it just click on the icon on the left, or PHPSimplex in the top menu.

PHPSimplex is able to solve problems using the Simplex method, Two-Phase method, and Graphical method, and has no limitations on the number of decision variables nor on constraints in the problems.

As the independent terms of all restrictions are positive no further action is required. Otherwise there would be multiplied by "-1" on both sides of the inequality (noting that this operation also affects the type of restriction).

The inequalities become equations by adding slack , surplus and artificial variables as the following table:

The following two methods are available for finding solution to a linear programming problem. 1) Graphic Method 2) Simplex Method When the decision variables involved are only 2, the LPP can be solved by using either of the two methods. But when the decision variables are > 2, only simplex method is used for finding solution.

FORMULATION OF LPP 1)The decision variables are x -- Number of hours of transportation by Type-1 cars y -- Number of hours of transportation by Type-2 cars 2) Objective function Minimise Z (total cost) = 5x + 4.50y 3) Structural constraints I)25 x + 15y >/= 2000 ii) x /= 0

Constraints form part of Linear Programming Problem Constraints may be relating to various resources like raw materials, Machinery, money, space, manpower,capacity,storage facilities, transport facilities, time, power The constraints inequalities developed for resources availability are called as resource constraints. The initial solution to a Linear Programming Problem when attempted to solve it by Simplex Method needs or requires an IDENTITY MATRIX in the Simplex Table.In case the LPP contains equality constraints ( constraints with = sign ) and / or > or = type constraints, without the introduction of artificial variables initial solution cannot be achieved. Therefore there is a need to introduce artificial variables. The artificial variables are introduced for the limited purpose of obtaining an initial solution. Artificial variables are introduced in case of both Maximisation and Minimisation problems. Artificial variables do not represent any quantity relating to the decision problem, they are driven out of the system and do not form part of final solution. In case artificial variables are there in the final solution it indicates a situation of infeasibility.