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2020101602465920201015222743hw 1 Final

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Subject
Management
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Kogod School of Business American University
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Homework
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Question 1. (21 points) OPTIMAL PRODUCT MIX AND WHAT-IF QUESTIONS
H&R Clock is a company that provides accounting services to individuals and businesses. The company
offers three types of services called service packages” for individuals and small business to file their tax
returns.
The deliverables and expectations of each service package is standard and do not vary from one client to
the next. Each service package requires input from staff members with three different expertise levels:
a junior accountant, a senior accountant, and a manager. The junior accountant has the initial contact
with a client to gather information. The senior accountant continues the work with the client to finalize
the tax returns. A manager then follows up with the client to track the response from IRS once tax forms
have been filed. Table-Q5-1 below shows the labor hour requirements per package. For instance, a
client who is receiving the basic service will spend 1 hour with a junior accountant, 5 hours with a senior
accountant, and 2 hours with a manager. The profit on each service package sold is also given in Table-
Q5-1. For instance, a basic service brings $110 in profit.
Service package
Labor-Hour Requirements (hours/service package)
Unit Profit
($ per package
sold)
Junior
Accountant
Senior
Accountant
Manager (M)
Basic
1
5
2
$110
Premium
2
5
4
$165
Deluxe
3
6
4
$143
Table-Q5.1. Labor hour requirements and unit profits of service packages.
The total labor hours available per month in each expertise area is given in Table-Q5-2. For instance, all
junior accountants are able to provide up to 1800 hours of service per month.
Expertise
Junior Accountant
Senior Accountant
Manager
Table-Q5.2. Monthly capacity
The company has already scheduled appointments with clients for the next month. The confirmed
number of client appointments is given in Table-Q5-3. These numbers show the number of packages the
company has committed to sell and is the minimum demand H&R Clock has to meet. However, the
company is heavily advertising and expects the demand to go up. The marketing department is very
successful in targeting new clients. With the marketing efforts, H&R Clock can serve a higher number of
customers in order to maximize the total profit next month.

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Service package
Minimum number of service packages to be
completed next month
Basic
20
Premium
25
Deluxe
30
Table-Q5.3. Confirmed demand for next month
You are asked to determine the optimal product mix (i.e., the monthly number of service packages to be
provided) that maximizes H&R Clocks profits for next month. You will formulate a linear programming
model to determine the optimal solution using Excel Solver.
NOTE: SHOW ALL YOUR WORK.
a) (3 points) What are the decision variables? How many decision variables are there? Clearly explain
the decision variables in English and provide the mathematical notation used in the algebraic
formulation of the decision problem.
Answer
Decision Variable describes the quantity that decision maker wants to determine. They are factors to
consider or when changed they affect decision made. In Our case accountant are our variables.
We let accountant number be X
We let our variable be X such that:
Our Decision variable is
X
1
X
2
X
3
,…..X
i
Values that variables can take:
x1, x2, x3 0
b) (2 points) What is the objective function? Clearly explain the objective function in English and
provide the mathematical formulation.

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Question 1. (21 points) OPTIMAL PRODUCT MIX AND WHAT-IF QUESTIONS H&R Clock is a company that provides accounting services to individuals and businesses. The company offers three types of services called “service packages” for individuals and small business to file their tax returns. The deliverables and expectations of each service package is standard and do not vary from one client to the next. Each service package requires input from staff members with three different expertise levels: a junior accountant, a senior accountant, and a manager. The junior accountant has the initial contact with a client to gather information. The senior accountant continues the work with the client to finalize the tax returns. A manager then follows up with the client to track the response from IRS once tax forms have been filed. Table-Q5-1 below shows the labor hour requirements per package. For instance, a client who is receiving the basic service will spend 1 hour with a junior accountant, 5 hours with a senior accountant, and 2 hours with a manager. The profit on each service package sold is also given in TableQ5-1. For instance, a basic service brings $110 in profit. Labor-Hour Requirements (hours/service package) Service package Unit Profit ($ per package sold) Junior Senior Manager (M) Accountant Accountant Basic 1 5 2 $110 Premium 2 5 4 $165 Deluxe 3 6 4 $143 Table-Q5.1. Labor hour requirements and unit profits of service packages. The total labor hours available per month in ...
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