A manufacturer of an industrial product has to meet the following shipping schedule:

The monthly production capacity is 30,000 units and the production cost per unit is $10. Because the company does not warehouse, the service of a storage company is utilized whenever needed. The storage company determines its monthly bill by multiplying the number of units in storage on the last day of the month by $3. On the first day of January the company does not have any beginning inventory, and it does not want to have any ending inventory at the end of March. Formulate a mathematical model to assist in minimizing the sum of the production and storage costs for the 3-month period. How does the formulation change if the production cost is 10x +10 dollars, where x is the number of items produced?

a. Identify the decision variables: What decision is to be made?

b. Formulate the objective function: How do these decisions affect the objective?

c. Formulate the constraint set: What constraints must be satisfied? Be sure to consider whether negative values of the decision variables are allowed by the problem, and ensure they are so constrained if required.