Thirst Quencher, Inc. (TQI), sells lemonade in city parks during the summer. TQI mixes a new batch of lemonade each morning. Once the TQI truck goes to the park, it is not feasible for it to return to its mixing facility to pick up more lemonade. TQI has determined that it costs $2.50 per gallon to make lemonade; it sells the lemonade in variously sized cups at an average price of $6 per gallon. Any lemonade that is not sold by the end of the day loses its fresh taste and is sold to a canned juice producer at a price of $1 per gallon. The demand for lemonade is approximately between LB and UB gallons per day. TQI wants to determine the amount of lemonade to produce each morning to maximize profit. TQIs cumulative demand distribution is given as

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