Part I. 3D Systems
3D Systems is a company producing personal protective equipment using 3D printers. The monthly
sales of their first year of operations are given in data file 3DSystems.xls (values in 1,000 USD, see CC,
Final Exam).
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop a three-month moving average forecast for the sales of 3D Systems. Include the Excel
results in your report.
c. Develop a forecast using exponential smoothing with α=0.2 for the sales of 3D Systems. Include the
Excel results in your report.
d. Calculate mean square error (MSE) for both three-month moving average and exponential smoothing
with α=0.2. Which one provides the better forecast based on MSE? Why?
Part II: MutuFund
MutuFund is planning to allocate $2,000,000 funds to Title loans, Payday loans, Unsecured Personal
loans, and Secured Personal loans. The annual rate of return (RoR) of each type of loan is shown in
table below. The management of MutuFund has decided to allocate at least 25% of total funds to Title
loans. In addition, the total allocation to Secured and Unsecured Personal loans cannot exceed 75% of
total funds. Furthermore, the amount allocated to Payday loans should be at least 30% of amount
allocated to Title loans.
Type of loan Unsecured Personal
loans
Secured Personal
loans
Payday loans Title loans
Rate of Return 12% 8% 9% 11%
a. Formulate a linear optimization model to determine the optimal amount of funds that should be
allocated to each type of loan to maximize the total annual return for the $2 million funds. Write down
the decision variables, objective function, and constraints.
b. Implement the optimization model in Excel spreadsheet and use the solver to obtain the optimal
solution. How much should be allocated to each type of loan? What is the total annual return? What is
the annual percentage return? Create screenshots of your Excel model and solver dialog box and include
them in your report.
c. Suppose that the rate of return on Title loans increases to 13%. How does the amount allocated to
each type of loan, total annual return, and annual percentage return change? Create screenshots of your
Excel model and solver dialog box and include them in your report.
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