Linear Programming

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A Linear Programming Problem is concerned with finding the optimal value (maximum or minimum) of a linear function (objective function) of several variables, subject to the conditions that variables a…

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An Objective Function is a linear function Z = ax + by (where a, b are constants) that needs to be maximized or minimized. It represents what we want to optimize, such as profit to maximize or cost to…

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Constraints are linear inequalities, equations, or restrictions on the variables of a linear programming problem. They represent limitations like available resources, storage capacity, or budget. Non-…

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A Feasible Region is the common region determined by all constraints (including non-negative constraints) of a linear programming problem. It represents all possible solutions that satisfy all given c…

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Feasible Solutions: Points within and on the boundary of the feasible region that satisfy all constraints. Infeasible Solutions: Points outside the feasible region that violate one or more constraints…

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An Optimal Solution is any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function. According to fundamental theorems, this optimal value occurs at a c…

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Let R be the feasible region (convex polygon) for a linear programming problem and Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), this optimal value must occu…

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Let R be the feasible region and Z = ax + by be the objective function. If R is bounded, then Z has both maximum and minimum values on R, and each occurs at a corner point of R. If R is unbounded, opt…