Pony express creations inc. (www,pony-ex.com) is a party hats, unmanly for the s
ID: 449383 • Letter: P
Question
Pony express creations inc. (www,pony-ex.com) is a party hats, unmanly for the season. (80 percent of their yearly sales occur over a six-week period.) One of their is the Elvis wig complete with sideburns and metallic The upcoming season Ryan the Express must make a single order owner of Pony Express, expects demand to be 25,000 demand forecast: The Elvis wig retails for S25, but Pony Express's wholesale price is S12. Their production cost is S6. Leftover inventory can be sold to discounters for $2.50. Suppose Pony Express orders 40,000 Elvis wigs. What is the chance they have to liquidate 10,000 or more wigs with a discounter? What order quantity maximizes Pony Express's expected profit wigs should ordered?Explanation / Answer
a.
If Pony express purchases 40,000 units, then it has to liquidate 10,000 or more units, provided if the demand is 30,000 units or less than that.
Now, consider the table given in the question. At F (30,000) the value is 0.7852. This implies that Pony express has 78.52% chance to liquidate 10,000 units or more than that.
b.
The underage cost can be calculated as:
CU = 12 – 6 = 6.
The overage cost is CO = 6 – 2.5 = 3.5.
Now, consider the critical ratio: 6 ÷ (3.5 + 6) = 0.6316.
Now, consider the table given in the question. At F (25,000) the value is 0.6289 and at F (30,000) the value is 0.7852.
Thus, 30,000 units would maximize Pony express expected profit.
c.
Calculation of order quantity that generates 90% fill rate:
Target lost sale = µ × (1-Fill rate) = 25,000 × (1-0.90) = 2,500.
Now, consider the table given in the question. At L (25,000) the value is 3908. And L (30,000) is 2502.
Thus, Pony express should order 30,000 units.
d.
If Pony express orders 50,000 units, then the expected loss is 63 units (consider the given table). Now, calculate the expected left over inventory.
Expected leftover inventory = Q – µ + Expected lost sales
= 50,000 – 25,000 + 63 = 25,063.
e.
If Pony express insists to have 100% in-stock probability then it would require an order quantity of 75,000 units. The expected lost sale is 2 units at this point (consider the given table).
Expected sales = Expected demand – Expected loss sales = 25,000 – 2 = 24,998.
Then, expected left over inventory = 75,000 – 24,998 = 50,002.
Now, calculate the expected profit.
Expected profit = (Price – Cost) × Expected sales – (Cost – Salvage value) × Expected left over inventory
= (12 – 6) × 24,998 – (6 – 2.5) × 50,002
= – 25,019.
Thus, it is clear that a 100% in-stock probability is not a profitable position. there would be a loss to Pony Express.