Problem $3$: The Transportation Problem

Three distribution centers with storage capacities of $25,40,$ and $30$ tons of food supply shipments to three relief camps. The maximum food requirements at the camps are estimated at $30,35,$ and $25$ tons, respectively. The transportation cost per ton from each distribution center to each relief camp is given in the table below. During the month of August, there is a $\backslash (20\backslash \%\backslash )$ increase in demand at each relief camp due to a rise in displaced populations. If needed, this additional demand can be met by purchasing food from a nearby supplier at a premium rate of $\backslash (\backslash$$ $1000\backslash )$ per ton. However, the supplier is unable to deliver directly to relief camp $3.$ The relief organization wishes to determine the most cost$-$effective plan for distributing food and purchasing additional supplies. Formulate the problem as a transportation model.

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