VF is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statement. Every December, VF sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 24 years of experience, VF categories their cases into the following groups:

Group 1 (new customers, easy): 15 percent of cases
Group 2 (new customers, complex): 5 percent of cases
Group 3 (repeat customers, easy): 50 percent of cases
Group 4 (repeat customers, complex): 30 percent of cases
Here “easy” versus “complex” refers to the complexity of the customer’s earning situation. In order to prepare the income tax statement, VF needs to complete the following set of activities. Activity times ( and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following activity times are expressed in minutes per income tax statement.
Group 1 – Filing 20 – Initial Meeting 30 – Preparation 120 – Review by Senior Accountant 20 – Writing 50
Group 2 – Filing 40 – Initial Meeting 90 – Preparation 300 – Review by Senior Accountant 60 – Writing 80
Group 3 – Filing 20 – Initial Meeting No Meeting – Preparation 80 – Review by Senior Accountant 5 – Writing 30
Group 1 – Filing 40 – Initial Meeting No Meeting – Preparation 200 – Review by Senior Accountant 30 – Writing 60
The activities are carried out by the following 3 people:
Administrative person : filing and writing
Senior Accountant: Initial Meeting and Review by Senior Accountant
Junior Accountant: Preparation
Assume all three persons work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 50 income tax statement arriving each month.
a. Which of the three persons is the bottleneck?
From my work I get the Sr. Accountant he is at 0.1332 monthly/income tax statementThe Jr. Accountant is 0.6555 monthly/income tax statement and the Administrative person is just at 0.3585 monthly/income tax statement. Am I Correct?

b. What is the (implied) utilization of the senior accountant? What is the (implied) utilization of the junior accountant? What is the (implied) utilization of the administrative person?
I getting Utilization of Sr. Accountant = 0.1332/(0.003+0.009) = 0.1332/0.012 = 1,110% Is this right?

a) The junior accountant is the bottleneck

b) The implied utilization of the employees:

Administration support person: 37.2%

3575min (how many hours he actually works)/ 9600min (his capacity, 60minx8hx20d) = 0.372

Senior accountant: 69.2%

6650min/9600min= 0.692

Junior accountant: 13.8%

1325min/9600min= 0.138

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Well, it seems like the senior accountant is working more than humanly possible! Utilization rates can often be misleading, especially when they go over 100%. In this case, it means the senior accountant is actually the bottleneck and cannot keep up with the workload. So, the implication here is that the senior accountant needs some help or more time to complete the tasks.

As for the junior accountant, their utilization is 0.6555/(0.005) = 131.1%. Again, it seems like they are working more than the available time, which suggests some extra support might be needed.

Lastly, the administrative person has a utilization of 0.3585/(0.003 + 0.009) = 39.84%. So, they seem to have some spare time on their hands.

In summary, the senior accountant is the bottleneck, the junior accountant is quite busy, and the administrative person has some free time to spare.

For the senior accountant, the utilization is calculated as the sum of the activities related to the senior accountant divided by the total available time per month:

Utilization of senior accountant = (Review by Senior Accountant time + Initial Meeting time) / (8 hours/day * 20 days/month) = (5 + 90) / (8 * 20) = 95 / 160 = 0.59375 or 59.375%

For the junior accountant, the utilization is calculated as the sum of the activities related to the junior accountant divided by the total available time per month:

Utilization of junior accountant = Preparation time / (8 hours/day * 20 days/month) = 300 / (8 * 20) = 300 / 160 = 1.875 or 187.5%

For the administrative person, the utilization is calculated as the sum of the activities related to the administrative person (filing and writing) divided by the total available time per month:

Utilization of administrative person = (Filing time + Writing time) / (8 hours/day * 20 days/month) = (20 + 50) / (8 * 20) = 70 / 160 = 0.4375 or 43.75%

So, the utilization of the senior accountant is 59.375%, the utilization of the junior accountant is 187.5%, and the utilization of the administrative person is 43.75%.

To determine which of the three persons is the bottleneck, you need to calculate the monthly rate at which each person completes the activities for the different groups of income tax statements.

For the administrative person:
- Filing time for Group 1: 20 mins/income tax statement
- Writing time for Group 1: 50 mins/income tax statement
Since the administrative person handles these activities for all groups, you can calculate their monthly rate by summing up the times for Group 1 and Group 4 (as they are both new customers):
Administrative person's monthly rate = (20 + 50) mins/income tax statement = 70 mins/income tax statement

For the senior accountant:
- Initial Meeting time for Group 2: 90 mins/income tax statement
- Review by Senior Accountant time for Group 2: 300 mins/income tax statement
Since the senior accountant handles these activities for Group 2, you can calculate their monthly rate using the percentage of Group 2 cases:
Senior Accountant's monthly rate = (90 + 300) mins/income tax statement * 0.05 (5% of cases) = 19.5 mins/income tax statement

For the junior accountant:
- Preparation time for Group 2: 300 mins/income tax statement
Since the junior accountant handles these activities for Group 2, you can calculate their monthly rate using the percentage of Group 2 cases:
Junior Accountant's monthly rate = 300 mins/income tax statement * 0.05 (5% of cases) = 15 mins/income tax statement

Now, refer to the calculations you mentioned to determine the bottleneck:
- Senior Accountant: 0.1332 monthly/income tax statement
- Junior Accountant: 0.6555 monthly/income tax statement
- Administrative Person: 0.3585 monthly/income tax statement

Based on these values, it seems that the junior accountant is the bottleneck, as they have the lowest monthly rate compared to the other two persons.

For part b, let's calculate the implied utilization for each person:

Utilization is defined as the actual working time divided by the available working time. In this case, assuming 8 hours per day and 20 days per month:

- Senior Accountant utilization: 0.1332 (monthly/income tax statement) * (50 income tax statements per month) * (60 mins/hour) / (8 hours/day * 20 days/month) = 83.25%
- Junior Accountant utilization: 0.6555 (monthly/income tax statement) * (50 income tax statements per month) * (60 mins/hour) / (8 hours/day * 20 days/month) = 408.44%
- Administrative Person utilization: 0.3585 (monthly/income tax statement) * (50 income tax statements per month) * (60 mins/hour) / (8 hours/day * 20 days/month) = 224.06%

Therefore, the implied utilization of the senior accountant is 83.25%, the junior accountant is 408.44%, and the administrative person is 224.06%.