Linear programming - method to achieve the best outcome such as maximum profit or
lowest cost in a mathematical model whose requirements are represented by linear
relationships.
Advantages:
 Can be solved using different methods, including the simplex method and the
interior-point method, allowing for flexibility in choosing the most suitable
approach.
 Well-structured and have efficient algorithms for solving them.
 Assists in making adjustments according to changing conditions
 Makes logical thinking and provides better insight into business problems
Disadvantages:
 It is not simple to specify the constraints even after the determination of a given
function. Specifying constraints is difficult There is a possibility that both
functions are linear.
 Determining the given function mathematically in a linear programming problem
is quite difficult.
 While solving a linear programming problem, the main problem is to determine
the coefficient values at each step.
 The assumptions made are not real since they are taken based on the elements in
the given situation.
 The solutions obtained can be real numbers all the time.
 When the objective function is determined, it is not easy to find social,
institutional, and other constraints.
Simplex programming - standard technique in linear programming for solving
an optimization problem, typically one involving a function and
several constraints expressed as inequalities. The inequalities define a polygonal region,
and the solution is typically at one of the vertices. The simplex method is a systematic
procedure for testing the vertices as possible solutions.
Advantages:
 Efficiency: The simplex method is often more efficient than other methods for
solving LP problems, especially when the solution is expected to be nondegenerate (not lying on the boundary of the feasible region).
 Well-established: The simplex method is a well-established and widely used
algorithm with a clear geometric interpretation.
Disadvantages:
 Not guaranteed to be polynomial-time: Although the simplex method is usually
efficient in practice, there are worst-case scenarios where it can take an
exponential number of steps to converge to the optimal solution.
 It is limited to LP only, it cannot be generalized to nonlinear problems
 Initialization: The choice of an initial feasible solution can affect the method's
efficiency, and finding a good initial solution can be challenging in some cases.