I DO NOT NEED THE CODE !!!! I NEED THE LINEAR PROGRAMMING MATHEMATICAL MODEL

2. Having determined a set of ten batches to be produced in the next period, a production manager for Textile manufacturer is looking for the best assignment of these batches to the different machines in the workshop. The five machines available in the workshop may each process any of these batches, but since they are all models from different years of manufacture the speed with which they process the batches changes from one machine to another. Furthermore, due to maintenance periods and readjustments, every machine may only work a certain mumber of hours in the planning period. The table below lists the processing times of the production batches on all machines and the capacities of the machines. Processing durations and capacities in hours Machine Production batches Capacity 1 2 3 4 5 6 7 8 9 10 1 8 15 23 8 16 25 17 18 2 15 7 23 22 11 11 12 10 17 16 19 3 21 20 22 24 10 24 9 21 14 24 4 2011 814 95 6 19 19 7 19 5 8 13 13 13 10 20 25 16 16 17 20 14 8 9 6 The production cost of a batch depends on the machine that processes it. The hourly usage cost for every machine depends on its technology, its age, its consumption of con- sumables (such as electricity, machine oil) and the personnel required to operate it. These differences are amplified by the variation in the processing durations of a batch depending on the machine. The table below lists the production costs in thousand TL. On which machine should each batch be executed if the production manager wishes to minimize the total production cost? Production cost depending on the assignment (in thousand TL) Machine Production batches 1 2 3 4 5 6 7 8 9 10 1 17 21 22 18 24 15 20 18 19 18 2 23 16 21 16 17 16 19 25 18 21 3 20 25 24 16 17 19 1918 4 19 19 22 22 20 16 19 17 21 19 5 18 19 15 15 21 25 16 16 23 15 16 16 1. Give an integer linear optimization model for the