The maintenance department of a manufacturing company schedules employment requirements for equipment preventive maintenance for each season. Labor needs can be met through hiring and firing based on the available number of technicians at the end of each month. The hiring manager is looking for the right policy in terms of employment levels in each month. Based on the forecasted number of preventive maintenance cases, the minimum number of technicians required from Aug, to Dec. is given in the following table Month Minimum # of required technicians Aug Sept. Oct Nov Dec: 5 7 8 4 6 New hiring in any month will incur a fixed cost of $400 plus $200 per technician per month A severance pay of $100 is also incurred for each fired technician Since technicians are difficult to hire the hiring manager is not willing necessarily to lay off technicians during the slack months. In other words, he has the choice of keeping excess technicians for one and/or more months to avoid new hiring for the upcoming months. Excess technicians will cost $300 per technician per month. There is no technician available before the month of August 1. Use dynamic programming to identify the optimal workforce size in each month such that the total cost is minimized. There is no need to consider the cost of tinng technicians at the end of Decin your calculations 2. Indicate the optimal number of hiring and firing in each month, in addition to the total cost of the optimal solution The maintenance department of a manufacturing company schedules employment requirements for equipment preventive maintenance for each season. Labor needs can be met through hiring and firing based on the available number of technicians at the end of each month. The hiring manager is looking for the right policy in terms of employment levels in each month. Based on the forecasted number of preventive maintenance cases, the minimum number of technicians required from Aug, to Dec. is given in the following table Month Minimum # of required technicians Aug Sept. Oct Nov Dec: 5 7 8 4 6 New hiring in any month will incur a fixed cost of $400 plus $200 per technician per month A severance pay of $100 is also incurred for each fired technician Since technicians are difficult to hire the hiring manager is not willing necessarily to lay off technicians during the slack months. In other words, he has the choice of keeping excess technicians for one and/or more months to avoid new hiring for the upcoming months. Excess technicians will cost $300 per technician per month. There is no technician available before the month of August 1. Use dynamic programming to identify the optimal workforce size in each month such that the total cost is minimized. There is no need to consider the cost of tinng technicians at the end of Decin your calculations 2. Indicate the optimal number of hiring and firing in each month, in addition to the total cost of the optimal solution