Solution

Elementary Linear algebra

Chapter 1.9

Exercise 4

$$0\le s\le 750,50\le t,t-s+600\ge 0$$

It is not possible to close the road from A to B for construction and keep traffic flowing on the other streets. If the road from A to B i.e., $x_1$ had a flow of $0$ then from the equation $x_1 =s+50$, $s$ must be equal to $-50$. This would correspond to a negative flow on $x_6$, which is invalid.

It can also be observed that node A has an inflow of 800. If the road from A to B is closed i.e., $x_1=0$, all the flow would move to F via $x_3$, but F has the maximum outflow rate 750.

Answer

(c) It is not possible to close the road from A to B for construction