Consider the following distance table with various parameters:

$\backslash$table$[[,1,2,3,4,5,$Demand$],[1,3,8,10,5,7,90],[2,9,2,12,10,6,85],[3,14,8,2,7,11,95],[4,10,13,19,1,3,70],[5,16,8,18,9,3,65],[$Facility Cost $($K$$),85,65,100,85,90,],[$Capacity$,350,200,360,370,150,],[\backslash$table$[[$Max # of Covered$],[$Sites$]],3,2,3,2,2,],[\backslash$table$[[$Min # of Covered$],[$Sites$]],1,1,2,1,1,]]$

There are four goals. The first goal is to minimize the total demand weighted distance, the second is to maximize the total capacity, the third is to maximize the covered demand, and the fourth is to minimize the total facility costs. Formulate the above problem as a Goal Programming model, subject to the constraint that each located facility must cover at least the minimum number of sites and, at most, the maximum number of sites, as shown in the above table. You are allowed to locate at most P$1$ facilities and at least P$2$ facilities. You must locate at least one facility at either site $1$ or $2$ and one facility at either site $4$ or $5.$ Let ${}_k$ denote the weight assigned to goal $k,k=1,2,3,$ and $4.$