Business, 27.07.2021 23:00 sarah1911

The Splash River has a flow rate of 2 x 106 m3 /d, of which up to 70% can be diverted into two channels where it flows through Splish County. These channels are used for transportation, irrigation, and electric power generation, with the latter two being sources of revenue. The transportation use requires a minimum diverted flow rate of 0.3 x 106 m3 /d for channel 1 and 0.2 x 106 m3 /d for channel 2. For political reasons it has been decided that the absolute difference between the flow rates in the two channels cannot exceed 40% of the total flow diverted into the channels. The Splish County Water Management Board has also limited maintenance costs for the channel system to be no more than $1.8 x 106 per year. Annual maintenance costs are estimated based on the daily flow rate. Channel 1 maintenance costs are estimated by multiplying $1.1 times the m3 /d of flow; while for channel 2 the multiplication factor is $1.4 m3 /d. Electric power production revenue is also estimated based on daily flowrate. For channel 1 this is $4.0 per m3 /d, while for channel 2 it is 3.0 m3 /d. Annual revenue from irrigation is also estimated based on the flow rate, but the flow rates must first be corrected for water loss in the channels previous to delivery for irrigation. This loss is 30% in channel 1 and 20% in channels 2. In both channels the revenue is $3.2 per m3 /d. Determine the flows in the channels that maximize profit.

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The Splash River has a flow rate of 2 x 106 m3 /d, of which up to 70% can be diverted into two chann...

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