Lisa, a recent MBA graduate, who specialized in business analytics, experiences a scenario at work where she sees an opportunity to utilize her learning from a decision analytics course. Lisa works as a middle$-$level manager for a huge computer giant which operates in several countries around the world. Lisa is in charge of the tech support group and she manages teams of tech support reps across multiple countries. As a part of her cost center$$s strategic planning initiative, she is tasked with developing a five$-$year staffing plan of tech support reps. Lisa believes that her department will need the following numbers of reps during each of the next five years: $60$ reps in year $1$; $70$ reps in year $2$; $50$ reps in year $3$; $65$ reps in year $4$; $75$ reps in year $5.$ At the beginning of each year, Lisa$$s department must decide how many reps to hire or fire. It costs $$4000$ to hire a rep and $$2000$ to fire a rep. A rep$$s salary is $$45,000$ per year. At the beginning of year $1$ Sarah has $50$ reps. A rep hired at the beginning of a year can be used to meet the current year$$s requirements and is paid full salary for the current year. Formulate and solve an optimization model that helps Lisa determine how to minimize the rep$$s salary, hiring, and firing costs over the next five years. $5$