Chapter 9.2, Problem 46E

Before beginning this exercise, the group needs to read and solve Exercise 40.

a A political group is planning a demonstration on 95lh Street between 113th Place and 117th Court for 5 p.m. Wednesday. The problem becomes one of minimizing traffic flow on 95lh Street (between 113th and 117ih) without causing traffic tie-ups on other streets. One possible solution is to close off traffic on 95lb Street between 113th and 117th (let $x_6=0$

). What can group members conclude about $x_7$

under these conditions?

b. Working with a matrix allows us to simplify the problem caused by the political demonstration, but it did not actually solve the problem. There are an infinite number of solutions; each value of $x_7$ we choose gives us a new picture. We also assumed $x_6$ was equal to 0; changing that assumption would also lead to different solutions. With your group, design another solution to the traffic flow problem caused by the political demonstration.