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The water-supply manager for Las Vegas needs to supply the city with at least 14 million gallons of potable water per day.
The supply may be drawn from the local reservoir or from a pipeline to an adjacent town.
The local reservoir has a maximum daily yield of 21 million gallons of potable water,
and the pipeline has a maximum daily yield of 11 million gallons.
By contract, the pipeline is required to supply a minimum of 6 million gallons per day.
If the cost for 1 million gallons of reservoir water is $460 and the cost for 1 million gallons of pipeline water is $315,
how much water should the manager get from each source to minimize daily water costs for the city?
What is the minimum daily water cost?
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The original formulation is/was mathematically and logically .
The corrected version (my correction) is below.
Needs to provide 14 mil. gallons for Las Vegas.
The reservoir has a max daily yield of 21 mil. gallons.
The pipeline has a max daily yield of 11 mil gallons.
The pipeline is required to supply >= 6 mil gallons per day.
cost for 1 mil. gallons: reservoir $460; pipeline $315.
Apply the most aggressive strategy, providing minimum cost: take as much water from
the cheaper source (which is pipeline) as possible, i.e. 11 mil. gallons;
take the rest from the reservoir, i.e. 14 mil. - 11 mil. = 3 mil. gallons.
The constraints are satisfied, and the minimum daily cost is
= 315*11 + 460*3 = 4845 dollars. ANSWER
Solved.