A Highway Patrol wishes to divide the effort of its on-duty officers among highway segments to maximise speeding reduction. The table below illustrates the data available. These are the upper bounds for the number of offices allowed to be assigned to a segment and the reduction potential for suppressing speeding on segments per officer allocated. Highway segment Upper bound Reduction Potential 1 5 12 2 3 8 3 3 7 4 4 6 5 3 10 (a) There are 20 officers available for an allocation. Formulate a linear programming problem to achieve the maximal total speeding reduction. [10 marks] (b) After finding an optimal allocation, it was noticed that some of the segments left without any officers allocated while for the rest of the segments the maximal allowed number of officers have been achieved. In other words, the solution found is not well balanced. Illustrate how the maxmin objective and linear programming technique can be used to obtain "better balanced" solutions. [7 marks] (c) Ignore (b). The officers available for patrolling belong to two different detachments, 10 officers in each detachment. It was decided that each team if allocated to patrol a highway segment, must include the members from two different detachments. Modify the model suggested in your answer to (a) to incorporate this new condition. [8 marks]