Find the shortest path from node $1$ to node $7$ by using dynamic programming approach for the

given network. You can see the routes for this network at below.

$d(1,2)=5,d(1,3)=9,d(1,4)=8$

$d(2,5)=10,d(2,6)=17$

$d(3,5)=4,d(3,6)=10$

$d(4,5)=9,d(4,6)=9$

$d(5,7)=19$

$d(6,7)=9$

a$.$ Draw the network of the problem

$(5$ points$).$

b$.$ Provide the recurrence formula for the problem.

$(5$ points$)$

c$.$ Write full solution for every stage and provide the optimal path and the shortest distance

$(15$ points$).$