solve it by details by hand please

Question $2$

Seven cities are being considered as potential locations for the construction of at most four wastewater treatment plants. The following table provides the data for the situation. Missing links indicate that a pipeline cannot be constructed.

Cost $($$$)$ of pipeline construction between cities per $1000ga\frac{l}{h}r$ capacity

$\backslash$table$[[$To$,1,2,3,4,5,6,7],[$From$,,100,,200,,50,],[1,,,,120,,150,],[3,400,,,,120,,90],[4,,,120,,120,,],[5,,200,,,,100,200],[6,,110,180,,,70,],[7,200,,,150,,,],[\backslash$table$[[$Cost$($$ million$)$ of$],[$plantconstruction$]],1\mathrm{.}00,1\mathrm{.}20,2\mathrm{.}00,1\mathrm{.}60,1\mathrm{.}80,0\mathrm{.}90,1\mathrm{.}40],[$Population $(1000$s$),50,100,45,90,75,60,30]]$

The capacity of a pipeline $($in gallons per hour$)$ is a direct function of the amount of wastewater generated, which is a function of the populations. Approximately $500$ gallons per $1000$ residents are discharged in the sewer system per hour. The maximum plant capacity is $100,000ga\frac{l}{h}r.$ Determine the optimal location and capacity of the plants.