Please refer to the following question:

Patricia, currently living in Vancouver, hires Andy to manage her Tim Hortons coffee shop in Waterloo. The profit of the shop depends on the level of Andy's effort (minimum, medium, maximum), and the state of nature (low demand or high demand) which is equally likely. The profit for each case is summarized as: Low demand High demand Minimum effort 20 40 Medium effort 40 60 Maximum effort 100 200 Andy's cost of effort is $0 for minimum effort, $10 for medium effort, and $30 for maximum effort. Both Patricia and Andy are risk-neutral. Without being able to directly monitor Andy's effort level from Vancouver, Patricia plans to offer one of the two contracts to Andy: (i) fixed wage of $30 with a bonus of 50% of the profit if the profit is above or equal to $200 or (ii) equal profit sharing (50-50%). What is the optimal level of Andy's effort under each contract and the corresponding income? Which contract would Patricia offer