Septembers production was set at 12,000 units. Varying production rate incurs some cost: production can be increased from one month to the next at a cost of $2 per unit and it can be decreased at a cost of $0.50 per unit. In addition, inventory left at the end of a month can be stored at a cost of $1 per unit per month. Given current demand, there will be no inventory at the end of September. No inventory is desired at the end of January. Formulate a linear program that minimizes the total cost (varying production rate + inventory costs) of meeting the above demand. And provide the AMPL code (model file ends with .mod and data file ends with .dat)(Look at the picture below for the entire problem and chart)

Problem 2. Sales forecasts for the next four months are (in thousand of units): October10 November16 December 10 January 12 September's production was set at 12,000 units. Varying production rate incurs some cost: production can be increased from one month to the nert at a cost of $2 per unit and it can be decreased at a cost of $0.50 per unit. In addition, inventory left at the end of a month can be stored at a cost of S1 per unit per month. Given current demand there will be no inventory at the end of September. No inventory is desired at the end of January. Formulate a linear program that minimizes the total cost (varying production rate + inventory costs) of meeting the above demand