A waste disposal system is shown below. Waste generated in cities $\backslash ($ A$,$ B $\backslash )$ and $\backslash ($ C $\backslash )$ are respectively $\backslash ($ b$\_\{$A$\}=50,$ b$\_\{$B$\}\backslash )\backslash (=30\backslash )$ and $\backslash ($ b c$=40\backslash )$ tons$/$day$.$ Transfer stations D and E are transshipment nodes. Landfills F and G can be assumed to have room for an unlimited amount of waste $(\backslash (\backslash$infty $\backslash )$ tons$/$day$).$ Costs $(\backslash (\backslash$$ $//\backslash )$ ton$)$ to move waste are shown on each link. All links have unlimited capacity. Formulate the problem as a MIN Cost Network Problem to move all the daily waste from the cities to the landfills.

$($a $-5$ pts $)$ Identify and properly define the decision variables of this problem.

$(\backslash (\backslash$mathrm$\{$b$\}-5\backslash$mathrm$\{$pts$\}\backslash ))$ Identify and properly define the objective function of this problem. Write it EXPLICITELY with all numbers and variables

$(\backslash (\backslash$mathrm$\{$c$\}-20\backslash$mathrm$\{$pts$\}\backslash ))$ Identify and properly define the constraints of this problem. Try to avoid obvious useless$/$redundant constraints

In addition to the MIN COST constraints in $($c$),$ also add these:

$($d $-5$ pts $)$ Assume that transfer station D must process at least $30$ tons$/$day of waste $($meaning that the total flow passing through this node should be at least $\backslash (30\backslash$ldots $\backslash )...).$ What constraint would you add to your formulation?

$($e $-5$ pts $)$ Assume that transfer station E can process at most $50$ tons$/$day of waste $($meaning that the total flow passing through this node should be at most $\backslash (50\backslash$ldots $\backslash ).).$ What constraint would you add to your formulation?