Question $1.$ Consider the cheesecake delivery problem indtroduced in the lecture notes where there are $11$ nodes: $1$ bakery and $10$ customers $($see lecture notes$).$

a$.$ How do you characterize a feasible solution if customers $3,5$ and $8$ should be visited consecutively $($the order does not matter$)$ and customers $1$ and $2$ must not visit consecutively?

b$.$ How many feasible solutions are there for part a$?$

c$.$ Write the corresponding constraints for parts a and a$.$