Question

Braum’s has a fine herd of cows that are content to produce milk at the rate of 500t+1000 gallons/hour (where t=hour of the day) from 4 am to 2 pm. Amish farmers milk their cows like crazy and load the milk onto tanker trucks bound for their pasteurization and bottling plant. The bottling plant can process milk at the rate of 5000 gallons per hour and they have a big tub they use to hold any milk that arrives that exceeds their processing capacity in a given hour. The tub holds 5000 gallons, and when it is full, any arriving trucks have to wait to dump their load. Now even though the trucks are large, when answering questions 3-5, treat trucks/milk as a continuous flow process – imagine a steady stream of tiny trucks making their way from farms to the plant.

At what time during the day will the trucks have to start waiting for some space to free up in the big tub? 4)

At what time is inventory at its zenith?

At what time will trucks stop waiting?

Now assume that the milk is picked up in trucks that hold 1,000 gallons each. What is the maximum number of trucks that are waiting?

How much milk is processed by the end of the day?

Answer 1

page-ol Answer Given details milk prodcution rate = 500€ +1000 gallons I how (where t= hour of the day) bottling plant milk process rate = 5000 gallons Tub which can hold = 5000 gallons. Tabulating the milks puodeution. hour of 5 am 6am il tom 8 am 10 am dan gallons of 1500 2000 2500 3000 3500 4000 mith llam | 12 am 1pm apm 4500 5000 5500 6000 The above table is calculating by substituting t=1,2,3- ...etc in equation 500€ +1000. At 5 om t= t hower 500 (1) 7000 1500 gallons At 6am t=2 hour 500 (2) 41000

page:oa = 1000 71000 = 2000 galtens At q am t = 3 hours = 500(3) 1000... = 1500 1000 = 2500 gallons At 8 am ; t. 4 hours = 500 (4) 41000 = 2000 + 1000 = 3000 gallons At aam t = 5 hours 2 500 (5) +1000 = 2500 +1000 = 3500 gallons Similarly 10 am t = 6 hours = 4000 gallons at it om tot hours = 4500 gallons at Qami ta 8 hours - 5000 gallons at (pm t=q hours = 5500 gallons at spm t= to howes = 6000 gallons

page:03 Truck need to wait for space when the storing tub and the processing plant both is full. . 5000 + 5000> Copacity & tub . . Capacity of plant = 10000 gallons At 9 am of the day truck need to wait - since sum of all the milk available at 9 am goes - beyond 10,000 gallons. ( 5amt 6amt fam + 8 am t9 am) = 1500 + 9000 + 2500 + 3000+ 3500 19,500 gallons. 4) At what time is inventory at its Zenith At a am the inventory is at Zenith level' and also at apm the Inventory is at peak fever At both these sentense the 2500 gallons is in waiting stock for processing (In truck)

page : 04 1 i 6 At what time will trucks stop waiting The truck will keep on moving nt q am it starts to wait.. . It will never stop waiting after till 8 am. that. 6) maximum number of trucks that are waiting 3 truecks will be waiting The maximum load waiting is 2500 gallons In foueck refer answer 4) so, 3 Trucks will be waiting since 1000 gallons is the capacity of the truck. 1) How much milk is processed by the end fihe day Total milk processed. = 15001 2000+ 2500+ 3000 + 3500+ 4000+ 4500 + 5000 + 5500+ 6000 = 37,500 gallons of milk.