Entry-level computer engineers in Seattle can be either high or low ability. Demand for engineers is perfectly competitive. Employers cannot distinguish the ability of any single engineer from another. An employer's total profit increase by 12 (thousand dollars) when a high-ability engineer completes a task, and by 5 (thousand dollars) when a low-ability one completes a task. High-ability engineers have utility function UH = W - 0.572, where W is wage (in thousand dollars) and T is number of tasks performed. Meanwhile, low-ability engineers have utility function U = W T. (a) (10 points) Suppose the employers design the following contract: "if you perform 5 tasks, you will be paid 5 (thousand dollars) per task; if you perform X number of tasks (X > 5), you will be paid 12 (thousand dollars) per task". Find Xmin, the minimal number of task X such that this contract achieves a separating equilibrium? (Leave your answer as it is. No rounding of Xmin required)