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.

Carefully explain all of the decision variables, constraints, objective function, and an appropriate solving method that you would choose. You *do not* need to solve your optimization model.