Problem 1 The demand for product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company's monthly demand. Unit Demand 300 400 500 600 Probability 0.20 0.30 0.35 0.15 a) What is the probability that the monthly demand is 400? What is the probability that the monthly demand is at least 400? b) If the company bases monthly orders on the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? c) What is the standard deviation in the monthly demand? d) What is the probability that the monthly demand is within one standard deviation of its expected value? (Hint: find P(µ – o ≤ X ≤ µ + µ)) e) Assume that each unit sold 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 (b) and the actual demand for the item is 500 units? (Hint: Profit = Revenue - Cost)

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