Problem $8($Adapted from Winston, $2004)$: City $1$ produces $500$ tons of waste per day, and city $2$

produces $700$ tons of waste per day. Waste must be incinerated at incinerator $1$ or $2,$ and each

incinerator can process up to $700$ tons of waste per day. The costs per ton to transport waste from each

city to each incinerator are given in the following table:

The cost to incinerate waste is $$\frac{25}{?}$ ton at incinerator $1$ and $$\frac{40}{?}$ ton at incinerator $2.$ Incineration

reduces each ton of waste to $0\mathrm{.}3$ ton of debris, which must be dumped at one of two landfills.

Each landfill can receive at most $200$ tons of debris per day. The costs per ton to transport debris from

each incinerator to each landfill are given in the following table:

Part a: Formulate an LP that can be used to minimize the total cost of disposing of the waste of both

cities. In this part, you should not use summation and "for every".

Part b: Formulate an indexed linear program $($i$.$e$.,$ using summation and "for every"$)$ to determine a

minimum$-$cost plan for disposing waste. You will need to define parameters to represent all of the data

associated with each city, incinerator, and landfill.

Part c: Solve the problem using an indexed model $($i$.$e$.,$ with summation and "for every"$)$ in AMPL$/$CPLEX

and report the obtained optimal solution.