Planning the distribution center $(35\%)$

A Chemical Company manufactures fertilizer in four plants, referred to as P$1,$ P$2,$ P$3,$ and P$4.$ Capacities in each day exist at the plants. The company plans to selectively build distribution centers in four places, which are designated as D$1$ D$2,$ D$3,$ and D$4.$ If a distribution center is built, there will be an operational cost; otherwise no operational cost occurs. At the distribution centers, no demand occurs and no capacity limits exist. Three warehouses, denoted as W$1,$ W$2,$ and W$3,$ have demand for the products for each day. The products are shipped from plants to distribution centers in the first stage, and in the second stage the products are shipped from distribution centers to warehouses. The units for capacity and demand are pounds of fertilizer, and the unit costs are given per pound. The daily warehouse demand, daily plant capacities, daily operational cost of distribution center, and unit cost to ship one pond of fertilizer is given in the tables below

$\backslash$table$[[,,$To$,],[,$Unit cost C$($i$,$ k$),$D$1,$D$2,$D$3,$D$4,$Capacities Cp$($i$)],[$From$,$P$1,1\mathrm{.}06,1\mathrm{.}32,1\mathrm{.}57,1\mathrm{.}24,2500],[,$P$2,0\mathrm{.}96,0\mathrm{.}87,1\mathrm{.}43,1\mathrm{.}63,2600],[,$P$3,1\mathrm{.}98,0\mathrm{.}87,0\mathrm{.}89,0\mathrm{.}99,2700],[,$P$4,1\mathrm{.}06,1\mathrm{.}67,1\mathrm{.}93,1\mathrm{.}07,2800],[,\backslash$table$[[$Operational cost$],[$OC$($k$)]],100,100,100,100,]]$

$\backslash$table$[[,,$From,$],[,$Unit cost $C(j,k),$D$1,$D$2,$D$3,$D$4,$Demand $Dm(j)$