During the next 3 months a company must meet (on time) the following demands for their products:

3,000 in month 1; 5,000 in month 2; 2,000 in month 3;

At the beginning of month one, 400 units of the product are on hand. The company currently has 80 workers, and each worker is paid $1500 per month. Each worker can work up to 160 hours a month, before receiving overtime. A worker can work up to 20 hours of overtime per month and is paid $13 per hour for overtime labor. At the beginning of each month, workers can be hired or fired. Each hired worker costs $1600, and each fired worker costs $2000. It takes 4 hours of labor and $15 of raw material to produce one unit of the product. Production in a given month can be used to meet that months demand. At the end of each month, a holding cost of $3 per unit of the product left in inventory is incurred. Write an optimization model to find the minimum cost production schedule and labor policy for the next three months.

You *do not* need to solve your optimization model. Just explaining decision variables, objective function, and appropriate solving method is enough.