Pony Express Creations Inc. is a manufacturer of party hats, primarily for the H
ID: 346141 • Letter: P
Question
Pony Express Creations Inc. is a manufacturer of party hats, primarily for the Halloween season. One of their popular products is the Elvis wig, complete with sideburns and metallic glasses. The Elvis wig is produced in China, so Pony Express must make a single order well in advance of the upcoming season. Ryan, the owner of Pony Express, estimates demand for this particular product during this year's selling season as follows: 1. With probability of 0.50, demand will be no more than 20,000 units With probability of 0.75, demand will be no more than 35,000 units With probability of 0.95, demand will be no more than 45,000 units. The Elvis wig retails for $25 each and its wholesale price is $12 each. Any leftover can be sold to discounters at $2.50 each Given the information above, carry out a marginal analysis for Ryan if he decides to order 20,000 units, or 35,000 units, or 45,000 units. Based on your calculation, which of these three order sizes would bring him the highest expected profit?Explanation / Answer
Suppose demand =d, order=x
profit/unit =25-12=13 $
total revenue (x-d)*2.5+25*d, total cost=12x
total profit (x-d)*2.5+25*d-12x>0
or d>0.42x eq1 or d=0.42x at no profit no loss situation.
with the mentioned probabilities we can conclude, probability of selling min 20000 is 50%,
probability of selling between 20000 and 35000 is 25%
probability of selling between 35000 to 45000 is 20% and
probability of selling above 45000 is 5%
Assuming order 20000, d should be greater than 0.42*20000 using eq1
d>8400
ie demand should be greater than 8400 for pony express to start making profit, max units for profit at 50%-20000-8400=11600
similarly assuming an order of 35000, d>14700 for pony express to make profit, max units for making profit at 50%-5300 max units for making profit at 25% probability=15000
similary assuming an order of 45000, d>18900 for pony express to make profit max units to make profit at 50% probability=1100, max units to make profit at 25% probability=15000, max units to make profit at 20%=10000
based on the data above, with highest probability maximimum profit making units are when order is 20000.
so order shall be placed for 20000