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 can be sold at the original cost of $2. 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 ______________________ 0.50

5 _________________________0.30

6 __________________________0.20

What is the optimal strategy for order quantity?

A) 400

B) 500

C) 600

D) Both B and C.

Explanation / Answer

let us assume that optimal stratergy for order quantity be X hunderd units

Expected no of orders = 4*0.50+5*0.30+6*0.20 = 4.7

lets us caluclate profit when he orders 1,2,3,4,5,6 hundred units

Expected profit when he orders 1 hundred unit = 1*800 - 1*200 = 600 . (no wastage in this case )

Expected profit when he orders 2 hundred unit = 2*800 - 2*200 = 1200 (no wastage in this case )

Expected profit when he orders 3 hundred unit = 3*800 - 3*200 = 1800 (no wastage in this case )

Expected profit when he orders 4 hundred unit = 4*800 - 4*200 = 2400 (no wastage in this case )

Expected profit when he orders 5 hundred unit = 0.5*(4*800)+0.5(5*800) - 5*200 = 2600

Expected profit when he orders 6 hundred unit = 0.5*(4*800)+0.3(5*800)+0.2(6*800) - 6*200 = 1600+1200+960-1200 = 2560

so answer is (B) 500

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