The demand for a particular product in the next four months is expected to be as follows: September: 800 units, October: 900 units, November: 1100 units, and December: 700 units.
Operating during regular hours the production capacity is 800 units/month. But overtime capacity is an additional 200 units/month. The selling price is the same irrespective of production mode, and the unit production costs are $10 and $12 for regular time production and overtime production, respectively.
In addition, there exists a storage cost of $1 per unit per month for each unsold unit held over. Formulate this problem as a linear program to determine a production plan that minimizes total production and storage costs.