Consider the following distance table:

$\backslash$table$[[,1,2,3,4,5,$Demand$],[1,3,8,10,5,7,65],[2,9,2,12,10,6,90],[3,14,8,2,7,11,100],[4,10,13,19,1,3,75],[5,16,8,18,9,3,80],[\backslash$table$[[$Facility Cost$],[($K$$)]],90,65,85,70,100,]]$

Solve each question independently. For each question, define your decision variables clearly. $($Time Limit: $60$ minutes$)$

Write a constraint ensuring that we can locate up to $P$ facilities.

Write a constraint ensuring that we can spend up to $$K($thousand$)$

Write an objective function for maximizing coverage demand.

Write an objective function of minimizing total facility costs.

Write all constraints ensuring the maximum distance between a site and the covering $($nearest$)$ facility is less than or equal to $W.$

Write all constraints, ensuring each site is covered by only one facility.

Write an objective function of minimizing the number of facilities being located.

Write all constraints ensuring that the demand$-$weighted distance between a site and the nearest facility is less than or equal to $W.$

Write all constraints, ensuring that each site can be covered by at least one facility.

Suppose we must locate one facility at either site $1,3,$ or $5$ and must locate one facility at either site $2$ or $4.$ Write all constraints ensuring the above conditions.