Problem:
Processing passport forms consists of two activities: 1. Data verification (DV) where the data provided by individuals are verified for its correctness and 2. Data Entry (DE) where the data is entered into a computer. During the next 3 weeks the following number of forms will arrive: week 1, 50,000; week 2, 30,000; and week 3, 60,000. The passport office (PO) can hire employees every week for the rest of the project duration who work for 40 hours per week and are paid $700 per week. Data verification of a form requires 30 minutes and data entry of a form requires 15 minutes. Each week an employee is assigned either for data verification or for data entry. PO must complete processing of all forms by the end of week 5 and wants to minimize the cost of completing the task.
For both (a) and (b) define all decisions variables and constraints clearly.
(a) Formulate a Linear Programming model that will determine how many employees should be hired each week and how the employees should be assigned to different tasks over the next 5 weeks.
(b) The PO has a space constraint in their office and can accommodate a maximum of 800 employees on any given week simultaneously. If the number of employees exceeds 800 in any week, then PO has to rent additional space that would cost them $5000 per week. Make necessary changes to your formulation in (a) to include this additional constraint.