A town requires a total water supply of at least 10,000 m^3/day. The water can b

Question

A town requires a total water supply of at least 10,000 m^3/day. The water can be blended from 3 sources: Source A - a well field with a maximum capacity of 8,000 m^3/day and a nitrate concentration of 36g/m^3 at a cost of $2/m^3. Source B - a reservoir that can supply 6,000 m^3/day with no nitrate at a cost of $5/m^3. Source C - a river that can supply 3,000 m^3/day with a nitrate concentration of 5g/m^3 at a cost of $7/m^3. The nitrate concentration in the finished water must be less than the contaminant limit of 10g/m^3. The town decides that the it will take the same percentage of available water from each source. End users of the water pay $4/m^3 to the town. Formulate, but do not solve the LP problem that can be used to determine the amount of water to be taken from each source that will provide the town the water it needs at the lowest cost.

Explanation / Answer

A +B+C = 10000 m3

2A + 5B + 7C = $ 40,000

36A + 5C < 100000

A < 8000, B <6000, C<3000

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