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 6000 batches per month. A 12 hour shift costs RI 70000 per month and can produce up to 8000 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 7000 , an additional team needs to be deployed to help

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 6000 batches per month. A 12 hour shift costs RI 70000 per month and can produce up to 8000 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 7000 , 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 2000 batches. Changing from an 8-hour shift in one month to a 12-hour shift in the next month costs an additional RI 5000 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 12 hour 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 1500 batches in stock, and the inventory cost for the current stock does not need to be taken into consideration at the staff of month 1 . The amount in stock at the end of month 12 should be at least 3000 units. The demand for the company's product in each of the next 12 months is forecast to be as shown below: Please provide the matlab code for the production plan. Please include the total cost in the code as well. Give out all objective functions and constraints as well