Consider the convex separable problem of Fig. 8.22, where each arc cost function ![](https://test.transtutors.com/qimg/8bb7b26c-74c6-45ce-9ef6-994836690096.png)
(a) Find the optimal solution and verify that it satisfies the optimality condition of Prop. 8.2.
(b) Derive and solve the dual problem based on the first formulation of Section 8.7.
![](https://test.transtutors.com/qimg/47559f3c-6466-427a-899c-cf3c1b290cd2.png)