![]() Otherwise, the objective function has no solution.Įxamples on LPP using Corner Point MethodsĮxample 1: Solve the given linear programming problems graphically: n is the minimum value of the objective function if the open half plan is got by the ax + by Otherwise, the objective function has no solution. N is the maximum value of the objective function if the open half plan is got by the ax + by > N has no common point to the feasible region. ![]() Or if the feasible region is unbounded then: Step 5: If the feasible region is bounded then N and n are the maximum and minimum value of the objective function. ![]() Assume N and n denotes the largest and smallest values of these points. Step 4: Now evaluate the objective function at each corner point of the feasible region. Step 3: Find the coordinates of the feasible region(vertices) that we get from step 2. Step 2: Now plot the graph using the given constraints and find the feasible region. Step 1: Create mathematical formulation from the given problem. To solve the problem using the corner point method you need to follow the following steps: We can solve linear programming problems using two different methods are, Graphical Solution of a Linear Programming Problems If there is no point in common in the linear inequality, then there is no feasible solution.If we have to find minimum output, we consider the outermost intersecting points of all equations.If we have to find maximum output, we have to consider the innermost intersecting points of all equations.Optimal(Most Feasible) Solution: Any point in the emerging region that provides the right amount (maximum or minimum) of the objective function is called the optimal solution. Any point outside the scenario is called an infeasible solution. The region other than the feasible region is known as the infeasible region.įeasible Solutions: These points within or on the boundary region represent feasible solutions of the problem. Optimization problem: A problem that seeks to maximization or minimization of variables of linear inequality problem is called optimization problems.įeasible Region: A common region determined by all given issues including the non-negative (x ≥ 0, y ≥ 0) constrain is called the feasible region (or solution area) of the problem. General Constraints: x + y > 40, 2x + 9y ≥ 40 etc.Non-Negative Constraints: x > 0, y > 0 etc.The variables x and y are called the decision variable.Ĭonstraints: The restrictions that are applied to a linear inequality are called constraints. Objective function: The direct function of form Z = ax + by, where a and b are constant, which is reduced or enlarged is called the objective function. Some commonly used terms in linear programming problems are, ![]() Transportation Problem: In these problems, we have to find the cheapest way of transportation by choosing the shortest route/optimized path. Our main objective in this kind of problem is to minimize the cost of diet and to keep a minimum amount of every constituent in the diet. And we have to find an optimal solution to make a maximum profit or minimum cost.ĭiet Problem: These problems are generally easy to understand and have fewer variables. Manufacturing Problem: In this type of problem, some constraints like manpower, output units/hour, and machine hours are given in the form of a linear equation. There are mainly three types of problems based on Linear programming they are, Role of Mahatma Gandhi in Freedom Struggle. ![]()
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