The personnel department of the A$\backslash$&M Corporation wants to know how many workers will be needed each month for the next $4$ month production period. The demands would be $1250,1100,950,900$ in months July, August, September, October. The inventory on hand at the end of June was $500$ units. The company wants to maintain a minimum inventory of $300$ units each month. Each unit requires $5$ employee hours. There are $20$ working days each month, and each employee works an $8-$hour day. The workforce at the end of June was $35$ workers. The workers can also work overtime, but overtime cannot exceed $30\%$ of the regular time in each month. Overtime costs an additional $$20$ per unit produced. Hiring costs $$2500$ per employee, firing costs $$4000$ per employee, payroll costs $$3000$ per employee per month, and inventory holding cost is $$100.$ Formulate the problem as an LP$.$