SOLUTION MANUAL FOR b b
Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon
b b b b b b b b b b b
Chapter 2-19
b b
Chapter 2 b
The Process View of the Organization
b b b b b
Q2.1 Dell b
The following steps refer directly to Exhibit 2.1. b b b b b b b
#1:For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
b b b b b b b b b b b b
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
b b b b b b b b b b b b
26,442$/ year
#3: Inventory turns = = 66.105 turns per year 400$
b b b
b b b b b b b b b
40% per year
#4: Per unit Inventory cost = = 0.605% per year
b b
b b b b b b b b
66.105 per year b b
Q2.2. Airline b
We use Little’s law to compute the flow time, since we know both the flow rate as well as the
b b b b b b b b b b b b b b b b b b b
inventory level:
b b
Flow Time = Inventory/Flow Rate =35 passengers/255 passengers per hour =0.137 hours
b b b b b b b b b b b b b b b
= 8.24 minutes b b
Q2.3 Inventory Cost
b b
(a) Sales= $60,000,000 per year/$2000 per unit =30,000 units sold per year b b b b b b b b b b b b b b
Inventory = $20,000,000/$1000 per unit = 20,000 units in inventory
b b b b b b b b b b b b
Flow Time = Inventory/ Flow Rate = 20,000/30,000 per year = 2/3 year = 8 months Turns =
b b b b b b b b b b b b b b b b b b b b b
1/Flow Time =1/(2/3 year) =1.5 turns per year
b b b b b b b b b b b b b
Note: we can also get this number directly by writing: b b b b b b b b b b Inventory turns = COGS/ Inventory b b b b b
(b) Cost of Inventory: 25% per year/1.5 turns =16.66%. For a $1000 product, this would
b b b b b b b b b b b b b b b
make an absolute inventory cost of $166.66.
b b b b b b b b
Q2.4. Apparel Retailing
b b
(a) Revenue of $100Mimplies COGS of $50M (because of the 100% markup). b b b b b b b b b b b
Turns = COGS/ Inventory = $50M/$5M =10 . b b b b b b b b b
(b) The inventory cost, given 10 turns, is 40%/10 = 4% . For a 30$ item, the inventory cost
b b b b b b b b b b b b b b b b b
is 0.4$30 = $1.20 per unit . b b b b b b b b
Q2.5. La Villa b b
(a) Flow Rate = Inventory/ Flow Time =1200 skiers /10 days = 120 skiers per day b b b b b b b b b b b b b b b b
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing b b b b b b b b b b b b b b b b b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, This year: on any given day, 20% (1 of 5) of skiers are on their first day of skiing
b b b b b b b b b b b b b b b b b b
Average amount spent in local restaurants (per skier) b b b b b b b
Last year = 0.1$50+0.9$30 = $32 This
b b b b b b b b
year = 0.2$50+0.8$30 =$34
b b b b b b b
%change =($34−$32)/$32 =6.25%increase
b b b b b b b b b
Q2.6. Highway
b
We look at 1 mile of highway as our process. Since the speed is 60 miles per hour, it takes a car
b b b b b b b b b b b b b b b b b b b b b
1 minute to travel through the process (flow time).
b b b b b b b b b
There are 24 cars on ¼ of a mile, i.e. there are 96 cars on the 1 mile stretch (inventory).
b b b b b b b b b b b b b b b b b b b
Inventory = Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
b b b b b b b b b b b b b b b
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
b b b b b b b b b b b b b b b b
Q2.7. Strohrmann Baking
b b
The bread needs to be in the oven for 12 minutes (flow time). We want to produce at a flow rate
b b b b b b b b b b b b b b b b b b b b
of 4000 breads per hour, or 4000/60 = 66.66 breads per minute.
b b b b b b b b b b b b
Inventory = Flow Rate * Flow Time: Inventory = 66.66 breads per minute* 12 minutes Thus,
b b b b b b b b b b b b b b b
Inventory = 800 breads, which is the required size of the oven.
b b b b b b b b b b b b
Q2.8. Mt Kinley Consulting
b b b
We have the following information available from the question:
b b b b b b b b
Level Inventory (number of consultants at b b b b Flow Time (time spent at that b b b b b
that level) b level)
Associate 200 4 years b
Manager 60 6 years b
Partner 20 10 years b
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory = Flow
b b b b b b b b b b b b b b b
Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate is 50
b b b b b b b b b b b b b b b b b b
consultants per year, which need to be recruited to keep the firm in its current size (note:
b b b b b b b b b b b b b b b b b
while there are also 50 consultants leaving the associate level, this says nothing about how
b b b b b b b b b b b b b b b
many of them are dismissed vs how many of them are promoted to Manager level).
b b b b b b b b b b b b b b b
(b) We can perform a similar analysis at the manager level, which indicates that the flow rate
b b b b b b b b b b b b b b b
there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level,
b b b b b b b b b b b b b b b b b b
we need to promote 10 associates to manager level (remember, the firm is not recruiting
b b b b b b b b b b b b b b b
to the higher ranks from the outside). Hence, every year, we dismiss 40 associates and
b b b b b b b b b b b b b b b
promote 10 associates to the manager level (the odds at that level are 20%)
b b b b b b b b b b b b b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the
b b b b b b b b b b b b b b b b
same calculations as before). Thus, from the 10 manager cases we evaluate every year, 8 are
b b b b b b b b b b b b b b b b
dismissed and 2 are promoted to partner (the odds at that level are thereby also 20%).
b b b b b b b b b b b b b b b b
In order to find the odds of a new hire to become partner, we need to multiply the promotion
b b b b b b b b b b b b b b b b b b
probabilities: 0.2*0.2 = 0.04. Thus, a new hire has a 4% chance of making it to partner.
b b b b b b b b b b b b b b b b b
Q2.9. Major US Retailers
b b b
a. Product stays on average for 31.9 days in Costco’s inventory b b b b b b b b b
b. Costco has for a $5 product an inventory cost of $0.1311 which compares to a b b b b b b b b b b b b b b
$0.2049 atWal-Mart b b
Q2.10. McDonald’sb
a. Inventory turns for McDonald’s were 92.3. They were 30.05 for Wendy’s. b b b b b b b b b b
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about b b b b b b b b b b b b b
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. b b b b b b b b b b b b b b
Q2.11. BCH b
I=400associates, T=2years. R = I/T = 400associates/2 yrs = 200associates/ yr.
b b b b b b b b b b b b b b b b b b b b b b b b
Q2.12. Kroger b
Turns = R / I = 76858/ 6244 =12.3 b b b b b b b b b
Matching Supply with Demand: An Introduction to Operations Management 5e
b b b b b b b b b
Solutionsto ChapterProblems b b b
Chapter 3 b b
Understanding the Supply Process: Evaluating Process Capacity b b b b b b
Q3.1 Process Analysis with One Flow Unit
b b b b b b
(a) Capacity of the three resources in units per hour are 602 /10 =12 , 601/ 6 =10; 603
b b b b b b b b b b b b b b b b b
/16 =11.25 . The bottleneck is the resource with the lowest capacity, which is resource
b b b b b b b b b b b b b b b
2. b
(b) The process capacity is the capacity of the bottleneck, which is 10 units/hr.
b b b b b b b b b b b b b
(c) If demand =8 units / hr , then the process is demand constrained and the flow rate is
b b b b b b b b b b b b b b b b b b b
8 units/hr b
(d) Utilization = Flow Rate / Capacity.For the three resources they are 8/12, 8/10, and b b b b b b b b b b b b b b b b b b b b b
8/11.25. b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, Q3.2 Process Analysis with Multiple Flow Units
b b b b b b
a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The demands b b b b b b b b b b b b b b
per hour of the three products are 40/8 = 5 , 50/8= 6.25and 60/8 = 7.5. The
b b b b b b b b b b b b b b b b b b b b b b b b b
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 =
b b b b b b b b b b b b b b b b b b b b b b
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So b b b b b b b b b b b b b b b b b
resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
b b b b b b b b b b b b b b
similarly evaluated. b b
b) The capacity of resource 3 is 60 /15 = 4 units per hour. Given the ratio of units produced must
b b b b b b b b b b b b b b b b b b b
be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units/ hr of B and
b b b b b b b b b b b b b b b b b b b b b b
6units/hrof C. b b b b b
Q3.3. Cranberry b
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per
b b b b b b b b b b b b b b b b b b b
hour. Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens while
b b b b b b b b b b b b b b b b b
trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour =
b b b b b b b b b b b b b b b b b b
400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.
b b b b b b b b b b b b b b b b b b b
(a) 200 barrels b
(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate of
b b b b b b b b b b b b b b
100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at
b b b b b b b b b b b b b b b b b b b
which time all waiting cranberries can be stored in the bins (no more truck waiting)
b b b b b b b b b b b b b b b
(c) It will take another 2 hours until all the bins are empty
b b b b b b b b b b b
(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate
b b b b b b b b b b b b b b b b
4hours * 50barrels per hour = 200 barrels. For the remaining time that we receive incoming
b b b b b b b b b b b b b b b b
cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only
b b b b b b b b b b b b b
accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we
b b b b b b b b b b b b b b b b b b
get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in inventory. After
b b b b b b b b b b b b b b b b
2pm, we receive no further cranberries, yet we initially process cranberries at a rate of 125 barrels
b b b b b b b b b b b b b b b b b
per hour. Thus, it only takes 100 barrels/125 barrels/hour = 0.8hours = 48 minutes
b b b b b b b b b b b b b b b b
until all bins are empty. From then, we need another 2h until the bins are empty.
b b b b b b b b b b b b b b b
Q3.4. Western Pennsylvania Milk
b b b
We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
b b b b b b b b b b b b b b b b
gallons, yet we ship 10,000 gallons. Thus inventory is depleted at a rate of 5000 gallons per hour,
b b b b b b b b b b b b b b b b b b
which leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait.
b b b b b b b b b b b b b b b b b b
This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
b b b b b b b b b b b b b b b b b
(a) 1pm
(b) Clients will stop waiting when we have worked off our 25,000 gallon backlog that we are
b b b b b b b b b b b b b b b
facing at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop
b b b b b b b b b b b b b b b b b b b
waiting at 11pm (after 5 more hours).
b b b b b b b
(c) At 6pm, we have a backlog of 25,000 gallons, which is equivalent to 20 trucks
b b b b b b b b b b b b b b
(d) The waiting time is the area in the triangle
b b b b b b b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon
b b b b b b b b b b b
Chapter 2-19
b b
Chapter 2 b
The Process View of the Organization
b b b b b
Q2.1 Dell b
The following steps refer directly to Exhibit 2.1. b b b b b b b
#1:For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
b b b b b b b b b b b b
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
b b b b b b b b b b b b
26,442$/ year
#3: Inventory turns = = 66.105 turns per year 400$
b b b
b b b b b b b b b
40% per year
#4: Per unit Inventory cost = = 0.605% per year
b b
b b b b b b b b
66.105 per year b b
Q2.2. Airline b
We use Little’s law to compute the flow time, since we know both the flow rate as well as the
b b b b b b b b b b b b b b b b b b b
inventory level:
b b
Flow Time = Inventory/Flow Rate =35 passengers/255 passengers per hour =0.137 hours
b b b b b b b b b b b b b b b
= 8.24 minutes b b
Q2.3 Inventory Cost
b b
(a) Sales= $60,000,000 per year/$2000 per unit =30,000 units sold per year b b b b b b b b b b b b b b
Inventory = $20,000,000/$1000 per unit = 20,000 units in inventory
b b b b b b b b b b b b
Flow Time = Inventory/ Flow Rate = 20,000/30,000 per year = 2/3 year = 8 months Turns =
b b b b b b b b b b b b b b b b b b b b b
1/Flow Time =1/(2/3 year) =1.5 turns per year
b b b b b b b b b b b b b
Note: we can also get this number directly by writing: b b b b b b b b b b Inventory turns = COGS/ Inventory b b b b b
(b) Cost of Inventory: 25% per year/1.5 turns =16.66%. For a $1000 product, this would
b b b b b b b b b b b b b b b
make an absolute inventory cost of $166.66.
b b b b b b b b
Q2.4. Apparel Retailing
b b
(a) Revenue of $100Mimplies COGS of $50M (because of the 100% markup). b b b b b b b b b b b
Turns = COGS/ Inventory = $50M/$5M =10 . b b b b b b b b b
(b) The inventory cost, given 10 turns, is 40%/10 = 4% . For a 30$ item, the inventory cost
b b b b b b b b b b b b b b b b b
is 0.4$30 = $1.20 per unit . b b b b b b b b
Q2.5. La Villa b b
(a) Flow Rate = Inventory/ Flow Time =1200 skiers /10 days = 120 skiers per day b b b b b b b b b b b b b b b b
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing b b b b b b b b b b b b b b b b b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, This year: on any given day, 20% (1 of 5) of skiers are on their first day of skiing
b b b b b b b b b b b b b b b b b b
Average amount spent in local restaurants (per skier) b b b b b b b
Last year = 0.1$50+0.9$30 = $32 This
b b b b b b b b
year = 0.2$50+0.8$30 =$34
b b b b b b b
%change =($34−$32)/$32 =6.25%increase
b b b b b b b b b
Q2.6. Highway
b
We look at 1 mile of highway as our process. Since the speed is 60 miles per hour, it takes a car
b b b b b b b b b b b b b b b b b b b b b
1 minute to travel through the process (flow time).
b b b b b b b b b
There are 24 cars on ¼ of a mile, i.e. there are 96 cars on the 1 mile stretch (inventory).
b b b b b b b b b b b b b b b b b b b
Inventory = Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
b b b b b b b b b b b b b b b
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
b b b b b b b b b b b b b b b b
Q2.7. Strohrmann Baking
b b
The bread needs to be in the oven for 12 minutes (flow time). We want to produce at a flow rate
b b b b b b b b b b b b b b b b b b b b
of 4000 breads per hour, or 4000/60 = 66.66 breads per minute.
b b b b b b b b b b b b
Inventory = Flow Rate * Flow Time: Inventory = 66.66 breads per minute* 12 minutes Thus,
b b b b b b b b b b b b b b b
Inventory = 800 breads, which is the required size of the oven.
b b b b b b b b b b b b
Q2.8. Mt Kinley Consulting
b b b
We have the following information available from the question:
b b b b b b b b
Level Inventory (number of consultants at b b b b Flow Time (time spent at that b b b b b
that level) b level)
Associate 200 4 years b
Manager 60 6 years b
Partner 20 10 years b
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory = Flow
b b b b b b b b b b b b b b b
Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate is 50
b b b b b b b b b b b b b b b b b b
consultants per year, which need to be recruited to keep the firm in its current size (note:
b b b b b b b b b b b b b b b b b
while there are also 50 consultants leaving the associate level, this says nothing about how
b b b b b b b b b b b b b b b
many of them are dismissed vs how many of them are promoted to Manager level).
b b b b b b b b b b b b b b b
(b) We can perform a similar analysis at the manager level, which indicates that the flow rate
b b b b b b b b b b b b b b b
there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level,
b b b b b b b b b b b b b b b b b b
we need to promote 10 associates to manager level (remember, the firm is not recruiting
b b b b b b b b b b b b b b b
to the higher ranks from the outside). Hence, every year, we dismiss 40 associates and
b b b b b b b b b b b b b b b
promote 10 associates to the manager level (the odds at that level are 20%)
b b b b b b b b b b b b b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the
b b b b b b b b b b b b b b b b
same calculations as before). Thus, from the 10 manager cases we evaluate every year, 8 are
b b b b b b b b b b b b b b b b
dismissed and 2 are promoted to partner (the odds at that level are thereby also 20%).
b b b b b b b b b b b b b b b b
In order to find the odds of a new hire to become partner, we need to multiply the promotion
b b b b b b b b b b b b b b b b b b
probabilities: 0.2*0.2 = 0.04. Thus, a new hire has a 4% chance of making it to partner.
b b b b b b b b b b b b b b b b b
Q2.9. Major US Retailers
b b b
a. Product stays on average for 31.9 days in Costco’s inventory b b b b b b b b b
b. Costco has for a $5 product an inventory cost of $0.1311 which compares to a b b b b b b b b b b b b b b
$0.2049 atWal-Mart b b
Q2.10. McDonald’sb
a. Inventory turns for McDonald’s were 92.3. They were 30.05 for Wendy’s. b b b b b b b b b b
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about b b b b b b b b b b b b b
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. b b b b b b b b b b b b b b
Q2.11. BCH b
I=400associates, T=2years. R = I/T = 400associates/2 yrs = 200associates/ yr.
b b b b b b b b b b b b b b b b b b b b b b b b
Q2.12. Kroger b
Turns = R / I = 76858/ 6244 =12.3 b b b b b b b b b
Matching Supply with Demand: An Introduction to Operations Management 5e
b b b b b b b b b
Solutionsto ChapterProblems b b b
Chapter 3 b b
Understanding the Supply Process: Evaluating Process Capacity b b b b b b
Q3.1 Process Analysis with One Flow Unit
b b b b b b
(a) Capacity of the three resources in units per hour are 602 /10 =12 , 601/ 6 =10; 603
b b b b b b b b b b b b b b b b b
/16 =11.25 . The bottleneck is the resource with the lowest capacity, which is resource
b b b b b b b b b b b b b b b
2. b
(b) The process capacity is the capacity of the bottleneck, which is 10 units/hr.
b b b b b b b b b b b b b
(c) If demand =8 units / hr , then the process is demand constrained and the flow rate is
b b b b b b b b b b b b b b b b b b b
8 units/hr b
(d) Utilization = Flow Rate / Capacity.For the three resources they are 8/12, 8/10, and b b b b b b b b b b b b b b b b b b b b b
8/11.25. b b
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
b b b b b b b b b b b b b b b b
McGraw Hill LLC. b b b
, Q3.2 Process Analysis with Multiple Flow Units
b b b b b b
a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The demands b b b b b b b b b b b b b b
per hour of the three products are 40/8 = 5 , 50/8= 6.25and 60/8 = 7.5. The
b b b b b b b b b b b b b b b b b b b b b b b b b
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 =
b b b b b b b b b b b b b b b b b b b b b b
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So b b b b b b b b b b b b b b b b b
resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
b b b b b b b b b b b b b b
similarly evaluated. b b
b) The capacity of resource 3 is 60 /15 = 4 units per hour. Given the ratio of units produced must
b b b b b b b b b b b b b b b b b b b
be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units/ hr of B and
b b b b b b b b b b b b b b b b b b b b b b
6units/hrof C. b b b b b
Q3.3. Cranberry b
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per
b b b b b b b b b b b b b b b b b b b
hour. Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens while
b b b b b b b b b b b b b b b b b
trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour =
b b b b b b b b b b b b b b b b b b
400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.
b b b b b b b b b b b b b b b b b b b
(a) 200 barrels b
(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate of
b b b b b b b b b b b b b b
100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at
b b b b b b b b b b b b b b b b b b b
which time all waiting cranberries can be stored in the bins (no more truck waiting)
b b b b b b b b b b b b b b b
(c) It will take another 2 hours until all the bins are empty
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(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate
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4hours * 50barrels per hour = 200 barrels. For the remaining time that we receive incoming
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cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only
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accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we
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get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in inventory. After
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2pm, we receive no further cranberries, yet we initially process cranberries at a rate of 125 barrels
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per hour. Thus, it only takes 100 barrels/125 barrels/hour = 0.8hours = 48 minutes
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until all bins are empty. From then, we need another 2h until the bins are empty.
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Q3.4. Western Pennsylvania Milk
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We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
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gallons, yet we ship 10,000 gallons. Thus inventory is depleted at a rate of 5000 gallons per hour,
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which leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait.
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This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
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(a) 1pm
(b) Clients will stop waiting when we have worked off our 25,000 gallon backlog that we are
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facing at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop
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waiting at 11pm (after 5 more hours).
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(c) At 6pm, we have a backlog of 25,000 gallons, which is equivalent to 20 trucks
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(d) The waiting time is the area in the triangle
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