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In this paper a load dispatch model for the system consisting of both thermal generators and wind turbines is developed. The stochastic wind power is included in the model as a constraint. It is shown that, under certain conditions, the presented model has a set of closed-form solutions. The availability of closed-form solutions is helpful to gain more fundamental insights, such as the impact of a particular parameter on the optimal solution. Moreover, the feasible ranges of optimal solutions are given in the case that the output power of thermal turbines is restricted. Furthermore, the probability distribution and the average of solutions are derived. This is called the wait-and-see approach in the discipline of stochastic programming. The present work shows that the effects of random wind speed on the generated power can be readily assessed.