pls solve a part completely

Demand 1 600 4 600 400 18 6 6 6 18 9 6 6 9 800 1. FCC Company manufactures a product for which the demand varies from month to month. The raw material and labor availability exhibit seasonal variations as shown in the following table. Capacity (tons) Cost of labor ($/ton) Maximum amount of raw Month Selling price Regular time Overtime Regular time Overtime material available (tons) (tons) ($/ton) 1200 2 1200 600 4 450 700 18 3 1200 600 4 425 600 4 800 500 6 9 1200 900 25 5 800 500 6 1300 900 25 800 500 9 1600 900 25 7 800 500 6 1600 800 25 8 500 6 9 1500 600 25 9 800 500 6 9 1300 800 25 10 1200 600 4 6 500 1200 30 11 1200 600 4 6 500 1100 30 12 1200 600 4 6 500 1400 30 The product manufactured during a month can be sold during the next month or later. Any unsatisfied demand has a backordering cost of $2 per ton per month. Storage costs for the product are $1 per ton from one month to the next. Raw material cannot be stored. It has to be used up in the month in which it is obtained. Operations begin in month 1 with a stock of 50 tons of the product. At the end of month 12, the company should have no backordered quantity and a stock of 50 tons of the product. (a) Formulate a linear programming model (or mixed integer programming model, if needed) to determine the optimal production plan for the company. Clearly, write the indices and parameters, define the decision variables, and write and explain the constraints and the objective function