• We consider the Butler Internet Company, which distributes a wireless router. Each router costs Butler $75 and sells for $125. Thus Butler realizes a gross profit of $125 - $75 = $50 for each router sold. The monthly demand for the router is described by a normal probability distribution with a mean of 115 units and a standard deviation of 25 units. Besides, the monthly administrative cost is a uniform distribution from $800 to $1050.
• Butler receives monthly deliveries from its supplier and replenishes its inventory to a level of Q at the beginning of each month. This beginning inventory level is referred to as the replenishment level.

  • If monthly demand is less than the replenishment level, an inventory holding cost of $15 is charged for each unit that is not sold.

    If monthly demand is greater than the replenishment level, a stock-out occurs and a shortage cost of $30 for each unit is incurred.

• Run the simulation for 100 months and calculate the average profit.