A machine cell is to be loaded to produce three part types. Machine A, B, and C are charged at the rate of 500, 400, and 300 TL per hour, respectively. All three machines have the capability of performing the given operations (unless marked by ""). Each machine can hold two tools and has 12 hours available. There are one unit of tool c and two units of tools a and b. The additional data is given in the table below. Unit Processing Time (min) Part Demand Operation Mach A Mach B Mach C Tool X 20 1 8 7 6 a 2 11 13 - b 3 9 9 Y 50 1 2 4 4 a 2 2 6 b Z 50 1 4 4 3 a 2 5 6 b 3 6 4 Assume that the operations of a part can be assigned to different machines. For instance, 5 units Operation 1 of Part X may be assigned to Machine A and the remaining 15 units may be assigned to Machine C. We define the decision variables as follows: Formulate the LP model for the loading problem by stating the objective function and specifying the constraints clearly. A generic model will not be accepted; you must formulate the objective function and each constraint separately using the data provided. Total processing time of Part Z on Machine B is {500} minutes. Cost of machines A, B, and C are 500/60, 400/60, and 300/60 per minute, respectively. Total time (in minutes) required by operation j of part i is calculated by multiplying the demand with unit processing time (e.g. total time required by operation 1 of part X on machine A is 208=160).