$2.(20$ points$)$ A company sells products in $3$ cities and has only enough budget to establish a total of exactly $5$ shops in these three cities. It is also required to have at least one shop in each city. The revenues $($in millions USD$)$ earned by opening shops in each city $($depending on how many shops are opened in a city, e$.$g$.$ if you open $2$ shops in City$-1,$ the company earns $75$ million USD$)$ is given below:

To solve this problem, use Dynamic Programming:

a$-)(5$ points$)$ Define the stage, state, decision variables and policy of the problem. b$-)(15$ points$)$ Determine the best allocation of $5$ shops in these $3$ cities to maximize total revenues.

$3.(35$ points$)$ A company can advertise through