The demand for Carolina Industries’ product varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company’s monthly demand:

Unit Demand ...... Probability

300 ........... 0.20

400 ........... 0.30

500 ........... 0.35

600 ........... 0.15

a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?

b. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?

c. What are the variance and standard deviation for the number of units demanded?