# Math

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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?

• Math -

a) The junior accountant is the bottleneck

b) The implied utilization of the employees:

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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