1. 63.210.207 Don Sutton Spring 2010

2. LP Basic Properties Objective Function – maximize/minimize profit/cost Resource Constraints – labor, money Decision Variables – alternative ways to use resources Linearity – objective and constraints are linear 2

3. Problem Formulation Completely understand the managerial problem being faced Identify the objective & constraints Define the decision variables Use the decision variable to write mathematical expressions for the objective function and the constraints 3

4. Product Mix Problem DeptTables (T)Chairs ©Available Hours Carpentry43240 Finishing21100 Profit per unit$70$50 4

5. Graphical Solution Isoprofit(cost) Method Corner Point Method Graph all constraints and find feasible solution Select specific profit(cost) line and graph it to find slope Move the line while maintaining slope. The last point it touches in the feasible region is optimum. Graph all constraints and find feasible solution Find all corner points in feasible range Compute profit at each feasible corner point Select the corner point with the best value in the objective function 5

6. Graphical Analysis Max profit 70T + 50C Subject to: 4T + 3C ≤ 240 2T + 1C ≤ 100 T,C ≥ 0 20 40 60 80 100 20406080100 Tables Chairs 6

7. Sensitivity Analysis In real life, there is uncertainty in Contribution margins Technical coefficients Resource availability How much can these change without affecting the optimal solution or change the variables in the solution 7