The buyer for Needless Markup, a famous “high end” department store, mustdecide on the quantity of a high-priced woman’s handbag to procure in Italy for thefollowing Christmas season. The unit cost of the handbag to the store is $28.50 andthe handbag will sell for $150.00. Any handbags not sold by the end of the seasonare purchased by a discount firm for $20.00. In addition, the store accountantsestimate that there is a cost of $0.40 for each dollar tied up in inventory, as thisdollar invested elsewhere could have yielded a gross profit. Assume that this costis attached to unsold bags only.a. Suppose that the sales of the bags are equally likely to be anywhere from 50to 250 handbags during the season. Based on this, how many bags should thebuyer purchase? (Hint: This means that the correct distribution of demand isuniform. You may solve this problem assuming either a discrete or a continuousuniform distribution.)b. A detailed analysis of past data shows that the number of bags sold is betterdescribed by a normal distribution, with mean 150 and standard deviation 20.Now what is the optimal number of bags to be purchased?c. The expected demand was the same in parts (a) and (b), but the optimal orderquantities should have been different. What accounted for this difference?
The buyer for Needless Markup, a famous “high end” department store, must
decide on the quantity of a high-priced woman’s handbag to procure in Italy for the
following Christmas season. The unit cost of the handbag to the store is $28.50 and
the handbag will sell for $150.00. Any handbags not sold by the end of the season
are purchased by a discount firm for $20.00. In addition, the store accountants
estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this
dollar invested elsewhere could have yielded a gross profit. Assume that this cost
is attached to unsold bags only.
a. Suppose that the sales of the bags are equally likely to be anywhere from 50
to 250 handbags during the season. Based on this, how many bags should the
buyer purchase? (Hint: This means that the correct distribution of demand is
uniform. You may solve this problem assuming either a discrete or a continuous
uniform distribution.)
b. A detailed analysis of past data shows that the number of bags sold is better
described by a
Now what is the optimal number of bags to be purchased?
c. The expected demand was the same in parts (a) and (b), but the optimal order
quantities should have been different. What accounted for this difference?
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