Solve the below problem:
Q: You manage two restaurants, Tender Steaks Inn (TSI) and Break For a Steak (BFS). Even though you run the establishments impeccably, you suspect that the Department of Health is out to get you, as they have been sending inspectors to both your restaurants on a daily basis and fining you for minor infractions. To ensure that a restaurant is operating without minor health violations seems to be a full time job, and you can spare only one employee to act as a full time "trouble-shooter." Thus, you must decide on a daily basis which restaurant you want "covered" by your trouble-shooter. Unfortunately, the Department of Health has two inspectors. On some days, both arrive at the same restaurant while on other days one arrives at each. If both inspectors arrive at a restaurant that isn't covered that day, the fine tends to be larger, since two inspectors are better at spotting minor infractions than one. The average fines you have been getting are shown in the following matrix.Health Inspectors Both at BFS Both at TSI One at Each Trouble-shooter at TSI $8,000 0 $2,000 BFS 0 $10,000 $4,000 What fraction of the time should your trouble-shooter be at each restaurant in order to minimize your expected fine? If you employ this strategy, what daily fine do you expect to pay?