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| Key Ideas 1. A linear programming (LP) model is a linearized mathematical representation of a system of relationships about a set of decision variables. The objective is to maximize or else to minimize a linear objective function, subject to a set of linear constraints and bounds for the variables. 2. The job of an analyst is to recognize the problem, formulate the model to solve the problem and supply the necessary input data. Because of the availability of computers and standardized LP codes, solving the model is now a fairly routine task. 3. An LP problem consists of an objective function, a set of constraints, plus a set of bounds for the decision variables. All are linear functions or inequalities. The objective function is a linear function with an unspecified value, Z. that is to be either maximized, if the problem deals with revenues or profits, or minimized, if it deals with costs. Because Z is not a specified constant, in graphical LP the objective function is represented by a family of parallel straight lines. The feasible space is the area of the first quadrant bounded both by the axes and by all of the constraints. A solution is a point in two-dimensional space, whether it satisfies the model or not. A feasible solution is a solution inside the feasible space. The optimal solution is the feasible solution that either maximizes or minimizes the objective function. The optimal solution is always a corner point of the feasible space. In order to find the exact values of x and y for a corner point, two constraint-boundary equations are solved simultaneously.4. Small problems with just two decision variables, are usually solved graphically. The text includes detailed step-by-step procedures for: (1) plotting the constraint boundaries that enclose the space of feasible solutions; (2) drawing the isoprofit (or isocost) lines that are parallel to the objective function; and (3) identifying the corner point of the feasible space at the intersection of two constraint boundaries, representing the optimum solution. 5. After the optimum is attained, sensitivity analysis can determine;
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