Four water use entities $($users $1-4)$ are to be supplied from one or more of four possible

sources $($A$-$D$).$ Sources A$,$ B$,$ and C cost Rs$.21{10}^6,$ and Rs$.30*10$

respectively, to develop. Source D costs only Rs$.12**{10}^6$ to develop but can only supply

customer $3.$ Sources C and D are mutually exclusive, meaning either, but not both, may be

selected. One, two or three water supply sources may be developed and used. A pipeline must

be constructed from each of the four customers to at least one of the four water supply

sources. A Source is developed only if at least one customer's pipeline is constructed to it$.$

Costs for constructing the four pipelines to the customers are provided below.

Each of the four customers are to be supplied from one of the four possible sources. The

problem is to decide: $(1)$ which sources to develop and $(2)$ if more than one source is

developed, which source will supply each customer. Use zero $-$ one LP to determine which

water supply sources to develop and which pipelines to construct to minimize total costs

$($costs of developing sources plus cost of constructing $4$ pipelines$).$