Please do not use computer program. It is only necessary to formulate the problem. Formulation steps are important to me. I will be glad if you solve with handwriting. URGENT.

4. SunTech Electronics produces DVD recorders in their city plant. The estimated demand for the product for next four periods is 3,000, 8,000, 5.000, and 2,000. At the beginning of period 1, SunTech has 50 workers. Sun Tech spends $1.500 to hire a worker and $5,000 to fire a worker. Workers are paid $12,000 per period. A newly hired worker can make up to 50 recorders per period, whereas a previously hired worker can make up to 80 recorders per period. Each DVD recorder is sold for $295. It costs $15 to hold a DVD recorder in inventory for a period. Assume that workers are hired and fired at the beginning of each period and the products produced in any period are available to meet demand of that period. Inventory at the beginning of period 1 is 500. Assume that demand is lost if it cannot be met from either current stock or production of current period. Develop a mathematical model for determining the worker level in each period in order to maximize Sun'Tech's profit