Show transcribed image textTranscribed image text: 1. You are a division manager and have two production facilities, A and B. The only variable input into production is the number of workers, and the relationship between productivity and the number of workers at each facility is given in the tables below. Note that productivity at Facility A is twice as large as productivity in Facility B at each and every number of workers. # of Workers 8 7 6 5 Facility A # of Production Workers 29 4 29.5 29 27 3 2 1 Production 24 20 15 8 Facility B # of # of Workers Production Workers Production 8 14.5 4 12 7 6 5 14.75 14.5 13.5 3 2 1 10 7.5 4 (a) You are paid based on the total value of production from the two facilities. Currently you are paid $100 for each unit produced at Facility A and $100 for each unit produced at Facility B. Suppose you have seven (7) workers which you can allocate to the two production facilities. Workers are on salary, cannot be fired, and can work at either production facility. How many workers should you assign to each facility? Please explain the rationale for your answer. (b) You have implemented the allocation from part (a). Some time later, your boss calls you up and says that headquarters is in need of more production from Facility B; on the following day, they are going to pay you $500 for each unit of production from Facility B, and will still pay $100 per unit of production from Facility A. How many workers should you assign to each facility? Please explain the rationale for your answer. (c) You’ve come to a decision regarding worker allocation under the new prices given in part (b) above, and call your facility managers to prepare for a possible change in the number of workers. The facility managers inform you that, for each worker you re-assign to Facility B, there is a $500 re-training charge that must be incurred. Given this knowledge, how many workers should you assign to each facility? Please explain the rationale for your answer.