Q3.4. Western Pennsylvania Milk
We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000 gallons, yet we ship 10,000 gallons. Thus, inventory is depleted at a rate of 5000 gallons per hour, which leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait. This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
(a) 1pm
(b) Clients will stop waiting when we have worked off our 25,000-gallon backlog that we are facing at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop waiting at 11pm (after 5 more hours).
(c) At 6pm, we have a backlog of 25,000 gallons, which is equivalent to 20 trucks
(d) The waiting time is the area in the triangle
- width: beginning of waiting (1pm) to end of waiting (11pm)=10 hours
- height: maximum number of trucks waiting: 20 (see part c above)
Hence, we can compute the area in the triangle as: 0.5*10hours*20trucks=100 truck* hours
The cost for this waiting is 50$/truck* hour * 100 truck hours=5000$