C ) Draw a single two - dimensional graph where the two axes correspond to the decision variables defined in part a . Then , for each goal , plot the region where the decision variables fully satisfy that goal . ( Hint : When plotting , treat the soft constraints you derived in part 6 just as you would regular " hard " constraints ) . Label the regions where each goal is satisfied . After completing this for all goals , use the graph to determine the optimal solution for this preemptive goal - programming problem ( Hint :" Consider each of the goals in order of priority )