A local retail store must place orders for Christmas in advance. Assume that eac

Question

A local retail store must place orders for Christmas in advance. Assume that each ornament costs the chain $2. Furthermore, assume that each ornament can be sold for a retail price of $8. If the ornaments are still on the shelves after Christmas, they cannot be sold. The probability distribution of consumer demand for these ornaments (in hundreds) during the upcoming Christmas season has been assessed by the market research specialists and is presented below. Finally, assume that the chain must purchase the ornaments in lots of 100 units.

Demand (in hundreds)

Probability

4

0.20

5

0.70

6

0.10

What is the optimal strategy for order quantity?

400

500

600

Both B and C.

Demand (in hundreds)

Probability

4

0.20

5

0.70

6

0.10

Explanation / Answer

Expected demand = 0.2*400 +0.7*500+0.1*600 = 80+350+60 = 490

If order quantity is 400,

Demand fulfilled = 400 ( Higher quantities will not be filled) Payoff = 400*( 8-2) = 2400

If order quantity is 500,

Average Demand fulfilled = 490 Payoff = 490*(6) - 10*2 = 2920

Going above 500 doesn't make sense because average demand is 490 only. Hence, answer is 500

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