based on the information above, if ryan predicts that the demand follows a norma

Question

based on the information above, if ryan predicts that the demand follows a normal distribution with a mean of 30,000 units and a standard deviation pf 5,000 units, what should he order to maximize his expected profit?

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: 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.

Explanation / Answer

cost = 12

retail price = 25

profit (P)= 25 - 12 = 13

left over sold at salvage value = 2.5

loss (L)= 12 - 2.5 = 9.5

P/(P+L) = 13/(13+9.5) = 0.5778

from standard z tables, we find the value of z for 0.5778

z = 2 (approx)

calculating the order value x = z*sd + mean = 2*5000 + 30000 = 40000

ryan should order 40000 units for maximizing his expected profit.

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