Neighborhood Hardware Ltd. acts as a central buying agent and distributor for a large number of retail hardware outlets in Canada. The product line is divided into six major categories, with a different buyer being responsible for every single category. One category is miscellaneous equipment for outdoor work around the home. The buyer for this group, Mr. Harry Lock, seeks assistance from you. In particular, Mr. Lock is concerned with the acquisition of a particular type of small snowblower that must be ordered several months before the winter. Mr. Lock has determined the snowblowers acquisition cost is $85.00 per unit and the selling price is $150.00 per unit. Any snowblowers unsold at the end of winter will be marked down to $51 per unit, ensuring a complete clearance and thus avoiding the prohibitive expense of storage until next season. The probability distribution of regular demand is estimated to be:
Number of Units: 300 400 500 600 700 800
Probability: 0.25 0.15 0.2 0.2 0.1 0.1
a. What is the expected demand?
b. What is the standard deviation of demand?
c. To maximize expected profit, how many units should you (using a discrete demand model) suggest to Mr. Lock to acquire?
d. What is the expected profit from your part c) strategy?
e. Suppose you decided instead to model demand using a normal distribution. The normal distribution will have the same mean and standard deviation as the above discrete distribution. With the normal model, what is the recommended order quantity, rounded to the nearest hundred units?
f. If the discrete distribution is the true one, what cost penalty is incurred by the use of the somewhat simpler normal distribution model?