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To process income tax forms, the Internal Revenue Service $($IRS$)$ first sends each form through the data preparation $($DP$)$ department, where information is coded for computer entry. Then the form is sent to data entry $($DE$),$ where it is entered into the computer. During the next $6$ weeks, the following numbers of forms will arrive: week $1,35,000$; week $2,30,000$; week $3,20,000$; week $4,25,000$; week $5,10,000$; week $6,50,000.$ All employees work $40$ hours per week and are paid $$550$ per week.

Data preparation of a form requires $15$ minutes, and data entry of a form requires $10$ minutes. Each week an employee is assigned to either data entry or data preparation. The IRS must complete processing all forms by the end of week $6$ and wants to minimize the cost of accomplishing this goal. Assume all employees are capable of performing data preparation or data entry but must be assigned to one task for an entire week at a time.

Question:

Formulate an LP model for the staffing problem. Use the spreadsheet provided to execute the model in Excel.

The solution obtained in part a$)$ may suggest imbalanced workload over time. That is$,$ a lot of forms are done in some week, while many fewer are done in others. Such a schedule is not practically appealing. To make sure a more balanced load over time, we impose a constraint that the forms processed at each step in each month should not exceed $30\%$ of the total number of forms to be processed. Modify the model $($in a separate workbook$)$ to find the new schedule.