The Lake Nocee Department Store has an opportunity to purchase a special shipment of X-mas tableware at $28 a set. These sets of tableware are to be sold for $35 as a special promotion during the store’s 40thanniversary sale. Nocee must purchase the items in units of a dozen sets. Tableware is not part of the store’s normal product lines, so if items are not sold during the X-mas cum 40th anniversary, they will be sold in the Bargain Basement for $22.20 per set. A sales consultant has estimated the following distribution of demand.
Demand (dozens) Probability
4 or less 0
5 0.10
6 0.15
7 0.25
8 0.20
9 0.15
10 0.10
11 0.05
12 0
Determine the optimal order quantity for Nocee regarding this item.
swer : optimal order quantity for Nocee = 8 dozec
Working notes for the above answer is as under
Co =$ 28-$ 22.20
=$5.80
Cu =$ 35-$28
=$ 7
P(d)*= Co /Cu+Co
=$ 5.80/$ 7+$5.8
=0.45
By referring to the cumulative probability column in Table it found the largest quantity with P(D) = 0.45 was 8, so he ordered 8 dozen sets of tableware.
| Demand (D) (Dozens) | Probability of Demand [P(d)] (Probability demand will equal this level) | Cumulative Probability of Demand [P(D)] (Probability demand will equal or exceed this level |
| 4 or less | 0 | 1 |
| 5 | 0.1 | 1 |
| 6 | 0.15 | 0.9 |
| 7 | 0.25 | 0.75 |
| 8 | 0.2 | 0.5 |
| 9 | 0.15 | 0.3 |
| 10 | 0.1 | 0.15 |
| 11 | 0.05 | 0.05 |
| 12 | 0 | 0 |
