$(35$p$)$ A city is divided into $3$ zones for security planning. Accordingly, it is planned to

distribute the $3$ new security personnel to these $3$ regions. The estimated number of

crimes that will occur when a certain number of new security guards are given to each region

is given in the table below.

a$)$ Accordingly, find out how many security

personnel should be assigned to each region in

order to minimize the total number of crimes,

using a dynamic programming approach.

b$)$ If the $3$rd Region had to be assigned more

security personnel than the $1$st Region, could

you use dynamic programming to solve the

problem? Please state with reasons.