1. You have taken over the management of a paper production firm. You find that the firm is contracted to deliver 3,000, 6,000, 5,000, and 2,000 reams of paper over the next four periods. At the moment, there are 500 reams of paper in stock. You want to devise a production schedule to deliver the paper over the next four periods. There are two ways to produce paper: An efficient machine that can produce paper at the cost of $1 per ream. Currently, this machine is calibrated to produce 4,000 reams of paper each period. It can be recalibrated from one period to the next to produce more paper at a cost of $3 per extra ream. (For example, if the current production level is 4,000 per period, and you wish to use the machine to produce 4,100 in the next period, this will cost an extra $300.) - It can also be recalibrated from one period to the next to produce less paper at a cost of $0.80 per ream. (For example, if the current production level is 4,100 per period, and you wish to use the machine to produce 4,000 in the next period, this will cost an extra $80.) An emergency machine that can produce paper at the cost of $1.40 per ream. This machine can produce any amount of paper in a period without any recalibration costs. Any paper that is left over at the end of a period incurs $0.05 per ream storage cost. You would like to reduce the output of the efficient machine to 3,000 reams per period at the end of the fourth period. Furthermore, you need at least 500 reams of paper in inventory by the end of the fourth period, and you pay an additional penalty of $0.15 per ream over 500. (a) (14 points) Formulate the optimal production schedule problem as a linear program. (b) (6 points) Please refer to the Jupyter Notebook for this question. Implement the model in Gurobi. Make sure that the model can take into account data of different sizes