# Assignment 4 (Group) You are required to answer these problems by building linear programming models

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Assignment 4 (Group)
Due Thursday, November 21st, at 6:00p.m.
This assignment consists of two problems. You are required to answer these problems by building linear programming models
and solving them using PuLP.
Each team needs to submit the following files through Canvas via a link under the “Assignment” section:
– An electronic copy of your python models. You should submit two separate files, one for each problem. The file name
should be the last names of all team members, listed alphabetically and separated by underscores followed by the
problem number; that is, lastname1_lastname2_lastname3_P1.ipynb and lastname1_lastname2_lastname3_P2. ipynb.
– An electronic copy of a short typed report. In the report you should
o Provide a network diagram representation of each problem
o Formulate (in math) linear program model for each problem (variables, objective function, constraints)
o State any assumptions you made if the problem statement is not 100% clear about certain aspects of the problem
o Include a clear printout of your python model.
o Present the optimal solution in an easy-to-communicate format
This is a group deliverable. Work with your designated team members only.
Problem 1 – Planning Cash
The chief financial officer for Eagle’s Beach Wear and Gift Shop is planning for the company’s cash flows for
the next six months. The following table summarizes the expected accounts receivables and planned payments
for each of these months (in \$100,000s).
Jan Feb Mar Apr May Jun
Accounts Receivable 1.50 1.00 1.40 2.30 2.00 1.00
Balances Due
Planned Payments 1.80 1.60 2.20 1.20 0.80 1.20
The company currently has a beginning cash balance of \$40,000 and desires to maintain a balance of at least
\$25,000 in cash at the end of each month. To accomplish this, the company has several ways of obtaining
short-term funds:
1. Delay Payments. In anymonth,the company’ssuppliers permititto delay any or all payments for one month.
However, for this consideration, the company forfeits a 2% discount that normally applies when payments
aremade on time. (Loss of this 2% discount is, in effect, a financing cost.) For example, if the company delays
the planned payment of \$180,000 for January, then the payment in February for this delayed amount will
be 180,000/.98 = 180,000 *1.02041 = \$183,673.47 approximately.
2. Borrow Against Accounts Receivables. In any month, the company’s bank will loan it up to 75% of the
accounts receivable balances due that month. These loans must be repaid in the following month and incur
an interest charge of 1.5%.
3. Short-Term Loan. At the beginning of January, the company’s bank will also give it a one-time 6-month loan
to be repaid in a lump sum at the end of June. Interest on this loan is 1% per month and is payable at the
end of eachmonth. The 1% monthly interest charge therefore applies to the entire amount, if any, actually
borrowed.
Assume the company earns 0.5% interest each month on cash held at the beginning of the month.
Question: Determine the least costly cash management plan (i.e., minimal net financing costs) for this 6-month
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period. What is the optimal solution?
Problem 2 – Workforce Planning
A software company is anticipating increased demand for its products. However, management is concerned about
the adequacy of their programmers to meet the increased demand given the history of workforce turnover (5
percent of the programmers leave the company at the end of each month).
Rather than hiring new workers, management is contemplating enrolling some or all of their programmers in a
month-long intensive training program. After the successful completion of the training program, a programmer
would receive an increase in salary and would also sign a contract not to leave the company for at least 6 months.
Trained programmers would therefore be immune from normal turnover.
Management believes that successful completion of the program would increase a programmer’s productivity by
20 percent and plans to implement a no-layoff policy to encourage participation. However, only 90 percent of the
programmers are predicted to complete the training program successfully. Those who enroll in training but do
not complete the program successfully will return to the workforce at their pre-training skill level. (For simplicity,
assume that they are not candidates for turnover during their training month and that the can enroll in the training
program again later.)
The monthly demand for untrained programmers for the next six months is shown in the table below. If trained
programmers are available, their higher productivity allows management to satisfy demand with fewer
programmers. For example, the demand in January can be satisfied with 100 untrained programmers, or with 82
untrained and 15 trained programmers (since 82+1.20*15=100).
Number of untrained programmers required
Month Jan Feb Mar Apr May Jun
Programmers 100 100 115 125 140 150
A programmer cannot be engaged in production and participate in the training during the same month. At the
beginning of January, there are 145 (untrained) programmers on the workforce. Monthly payroll costs to the
company are \$3000 per untrained programmer (engaged in either production or training program) and \$3300 per
trained programmer.
Questions:
(a) Determine a training schedule and a lay-off schedule for the months of January through June that meets the
workforce requirements at the minimum cost. What is the optimal cost? (Allow for fractional solutions.)
(b) If the company could shift demand from June to April (i.e., June demand=125 and April demand =150), would
the cost be higher or lower, and by how much?

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