Question

The Shady Farm Milk Company can process milk at a fixed rate of 6800 gallons/hour. The company’s clients request 107000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. - 6 p.m. The company starts producing at 8 a.m. and continues to work until all of the demand has been satisfied. How long does the client requesting milk at 6pm have to wait to have their _____ hours demand satisfied? (round answer to 2 decimal places

Answer 1

Processing rate, p = 6,800 gallons/hour

Demand rate, d = 107000/10 = 10,700 gallons/hour (from 8 am to 6 pm = 10 hours)

Backlog at 6pm = Total demand over 10 hours - total processing over 10 hours

= 10*(10700-6800)

= 39,000 gallons

Total hours required to complete processing of backlog = 39000/6800

= 5.74 hours