Roofers SA can operate either a normal, 8-hour shift or an extended, 12-hour shift for a month at a time. An 8-hour shift costs R90 000 per month and can produce up to 6 000 batches per month. A 12hour shift costs RI 70 000 per month and can produce up to 8 000 batches per month. The company can also choose not to produce any black ceramic tiles for a month, in which case there is no shift cost. (If the production line is not used for this product, it can be used by other teams to manufacture other products.) Raw materials for one batch cost R0.50. If production exceeds 7 000, an additional team needs to be deployed to help out at an additional cost of R30 000. If the company produces anything in a particular month, it must produce at least 2 000 batches. Changing from an 8-hour shift in one month to a 12-hour shift in the next month costs an additional RI 5 000 in setup costs. Changing from a month where there was no production to a month where there is production incurs an additional R25 000 setup cost. No extra cost is incurred in changing from a 12hour shift in one month to an 8-hour shift in the next month or changing from a month of production to no production in the following month. Currently, the production line for this product is operating a normal shift. Holding stock is risky because it can get stolen and costs R2 per batch per month. Assume the cost of inventory for any particular month is related to the amount m stock at the end of that month. There are currently 1 500 batches in stock, and the inventory cost for the current stock does not need to be taken into consideration at the staff of month l. The amount in stock at the end of month 12 should be at least 3 000 units. The demand for the company's product in each of the next 12 months is forecast to be as shown below:

month	1	2	3	4	5	6	7	8	9	10	11	12
demand	5000	6000	4500	2100	7500	5500	1000	6800	7300	5600	8000	6000

Write a production plan(using milp) using excel solver. Please show how to do all the calculations and give all the necessary constraints. For example the speadsheet must contain: Month (from 1 to 12) Production Decision (in batches) Shift Decision (8-hour or 12-hour) Setup Cost (for shift change or production start) Production Cost Inventory at the beginning of the month (starting with 1,500 batches) Inventory at the end of the month Total Cost Could you also please provide the ampl code for this..