what is difference between regular simplex method and dual simplex method
Simplex method used for maximization, where dual simplex used for minimization.
The simplex method is an algorithm used to solve linear programming problems, typically starting from a feasible solution and moving toward optimality by improving the objective function. In contrast, the dual simplex method begins with a feasible solution to the dual problem and iteratively adjusts the primal solution to maintain feasibility while improving the objective. The dual simplex is particularly useful when the primal solution is altered due to changes in constraints, allowing for efficient updates without reverting to a complete re-solution. Both methods ultimately aim to find the optimal solution but operate from different starting points and conditions.
The first approximation to is always integral and therefore always a feasible solution. Rather than determining a first approximation by a direct application of the simplex method it is more efficient to work with the table given below called the transportation table. The transportation algorithm is the simplex method specialized to the format of table it involves: i) finding an integral basic feasible solution ii) testing the solution for optimality iii) improving the solution, when it is not optimal iv) repeating steps (ii) and (iii) until the optimal solution is obtained.
Semplex
Simplex Method and Interior Point Methods
half-duplex communication of a data transmission method
LPP deals with solving problems which are linear . ex: simlpex method, big m method, revised simplex, dual simplex. NLPP deals with non linear equations ex: newton's method, powells method, steepest decent method
graphical method is applicable only for solving an LPP having two variables in its constraints , but if more than two variables are used, then it is not possible to use graphical method. In those cases, simplex method helps to solve such problem. In simple, in graphical method is used when the constraints contain two variables only. But simplex method can be used to solve constraints having more than two variables.
The auction method, depending on the type of method used, satisfies Pareto optimality for the following reason: it is always best in an auction to bid your own valuation for a good. In game theory terms, this means that bidding your monetary valution of the good is always a weakly-dominanted strategy. This implies that the winner of the bid will, ignoring monetary constraints, will always be the person with the highest valuation of the good (since they bid the highest). Pareto optimality occurs when no one can be made better off without making someone worse off. When the item belongs to the person/group who values it most, social welfare is optimised (this is also called the Hobbes Theorem). Thus, the auction method, with basic rules, satisfies Pareto optimality by assigning the good to the person who values it most.
The simplex method offers several advantages over graphical linear programming, particularly in handling higher-dimensional problems. While graphical methods are limited to two-variable scenarios, the simplex method can efficiently solve linear programming problems with multiple variables and constraints. It also provides systematic iteration towards the optimal solution, making it more suitable for complex and large-scale applications. Additionally, the simplex method can handle cases of degeneracy and multiple optima more effectively than graphical techniques.
When you have 3 variables or more. In paper, we can only draw 2 dimensional shapes.