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 each single category. One category is miscellaneous equipment for outdoor work around the home. The buyer for this group, Mr. Harry Lock, seeks assistance from a recently hired analyst, J. D. Smith, in the computer division of the company. In particular, he is concerned with the acquisition of a particular type of small snowblower that must be ordered several months before the winter. Smith, after considerable discussions with Lock, has the latter’s agreement with the following data:

Unit acquisition cost is $60.00/unit Selling price is $100.00/unit Any units unsold at the end of the winter will be marked down to $51/unit, ensuring a complete clearance and thus avoiding the prohibitive expense of storage until the next season. The probability distribution of regular demand is estimated to be Hundreds of Units, jo 3 4 5 6 7 8 Pj(jo) 0.1 0.1 0.4 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 Smith (using a discrete demand model) tell Lock to acquire?

d. What is the expected profit under the strategy of (c).

e. Suppose Smith instead decides to fit a normal distribution, having the same mean and standard deviation, to the above discrete distribution. With this 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 model?? Lp852