MODELING WITH LINEAR PROGRAMMING CHAPTER 2 1 ◦ A Linear Programming model seeks to maximize or minimize a linear function, subject to a set of linear constraints. ◦ The linear model consists of the following components: ◦ A set of decision variables that we seek to determine. ◦ An objective function that we need to optimize(maximize or minimize). ◦ A set of constraints that the solution must satisfy. 2 Two variable LP Problem First we discuss the graphical solution of a twovariable LP. Though two-variable problems hardly exist in practice, the treatment provides concrete foundations for the development of the general simplex algorithm 3 Example 4 Some constraints ◦ The daily demand for interior paint cannot exceed that for exterior paint by more than 1 ton. ◦ Also, the maximum daily demand for interior paint is 2 tons. Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit 5 6 The Graphical Analysis of Linear Programming The set of all points that satisfy all the constraints of the model is called a FEASIBLE REGION 7 8 9 The feasible solution space is ABCDEF in which all the constraints are satisfied (verify!). All points outside the boundary of the area ABCDEF are infeasible. 10 11