This article is to provide a model which controls production and inventory of single-period, single-product under random demand, in an attempt to obtain both production function and the production interval. The following assumptions hold: (1) sales occur at a certain time in the future, (2) product demand is a random variable, and (3) the cost of unit production is a linear function of production quantity in a unit time. The sensitivity analysis on key variables of the optimal solution is discussed.