Consider the following distance table:

$\backslash$table$[[,1,2,3,4,5,$Demand$],[1,3,8,10,5,7,100],[2,9,2,12,10,6,75],[3,14,8,2,7,11,80],[4,10,13,19,1,3,95],[5,16,8,18,9,3,70],[$Facility Cost $(K$$$),100,85,65,90,85,],[$Capacity$,400,350,200,360,370,],[$Max # of Covered Sites,$2,3,2,3,2,],[$Min # of Covered Sites,$1,2,1,2,1,]]$

Solve each question independently. Set $=95.$ For each question, define your decision variables clearly and write an objective as well as constraint$($s$).($Time Limit: $60$ minutes$)$

Write an objective function for maximizing the total capacity subject to $P.$ You should locate $P$ facilities.

Write an objective function for maximizing covered demand subject to the budget $K.$

Write an objective function for minimizing the number of facilites to be located, subject to all demands satisfied.

Write an objective function of minimizing total costs $(=$fixed cost $+$ costs for total demand weighted cost$)$ subject to the max and min # of covered sites.

Write an objective function of maximizing the total capacity, ensuring each site is covered by at least one facility.

Suppose we must locate at least one facility at either site $2,$ or $4$ and must locate at most one facility at either site $1,2$ or $5.$ Write an objective function for minimizing the total facility costs subject to the above constraints.