Problem 1 (27.5 points). For a given company, specifically the HR department, needs to identified the quantity of employees required each month for the next sixth-month production period. Based on past experience, the company is estimating that demand over the next six months will be as follow: Although the company estimated that they will end with 300 units, the inventory on hand at the end of December was 450 units. The company wants to maintain a minimum inventory of 200 units each month at a holding cost of $2 per unit, and would like to have 500 units on hand at the end of June. Each unit requires five employee hours to produce, there are 20 working days each month and each employee works eight hours per day. Each employee produces 32 units per month. The work force at the end of December was 25 employees. On average, each employee is paid $3,000 per month. Based on the effort of interviewing and training new employees, the company estimates that it costs $1,000 for each employee hired. Firing pay amounts to $500 per employee. a. (15 points). Determine a minimum inventory production plan that allows arbitrary hiring and firing. Determine planned production, number of employees needed, hires or fires. b. (8 points). Evaluate the costs (inventory holding, wages, hiring, firing) that will be