6. (15 pts) Consider the hair-dressing industry, where solons hire hairdressers. Each hairdresser works for only one solon. Each hairdresser is good at one particular hair style, which can be divided into 24 types. In other words, the hair style Wheel is like a 24-hour clock. Each solon enters the market and targets a certain type of customers. Each type of customers have a specic requirement for hair style. If a hairdresser does not match the solon's requirement, the hairdresser must spend money re-training her skill in order to close the gap. The cost of re-styling is $2 for each unit of hair style shift. For example, to go from style #3 to style #2, the cost is $2; to go from style #5 to style #2, the cost is $6. Each solon hires two hairdressers. There are two cities in the region: Smallville has 4 hairdressers and Bigburg has 12. The gross wage for each hairdresser is $60. Assume that hairdressers are evenly distributed around the hair style wheel. Compute the net wage for hairdressers in each of the two cities. Show steps for partial credit. (a) (10 pts) In Smallville, suppose the 4 hairdressers are in positions (0, 6, 12, 18), two solons will enter at positions (3, 15). What is net wage for a hairdresser in Smallville? (b) (5 pts) In Bigburg, suppose the 12 hairdressers are in positions (0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22), 6 solons will enter at positions (1, 5, 9, 13, 17, 21). What is net wage for a hairdresser in Bigburg