Optimally allocating a scarce resource such as water is a great example of how LP models can be used to $$save the world$.$ This is a simplified scenario that illustrates such a possibility.

Healing Rain Consulting has been charged with determining the optimal allocation of water to the $11$ regions listed below for the upcoming growing season for the Colorado River Watershed.

Data provided: Region name, the region$$s state, the historic water allocation $($in XXX cubic meters$),$ the societal value of water in that region $($per XXX Cubic meter$),$ the level of drought presently found in the region and the cost per XXX cubic meter allocated.

Parameters:

Goal: Maximize the societal value of water allocated to the $11$ regions. The measure is simply the value parameter for a region multiplied by the water allocated to that region, summed over all regions.

Restrictions:

You have a maximum of $6600$ XXX cubic meters to allocate.

You cannot allocate to a specific region more water than the historic values, but you also must allocate at least $400$ XXX Cubic meters to each region.

Total cost must be less than or equal to $28,000$ cost units.

Each state cannot have more than $25\%$ of the total water allocated $($do not make erroneous assumptions$).$ Likewise, each state cannot have less than $18\%$ of the total water allocated.

Water must be allocated to the regions such that the weighted average of the $$Drought$$ parameter is at least $5\mathrm{.}8$ units. Weighted averages calculated as usual.

At the very end of modeling, force integer water allocations.