1. The J&B Card Shop sells calendars featuring a different Colonial picture for
ID: 449531 • Letter: 1
Question
1. The J&B Card Shop sells calendars featuring a different Colonial picture for each month. The once-a-year order for each year’s calendar arrives in September. From past experience the September-to-July demand for the calendars can be approximated by a normal distribution with µ = 500 and standard deviation = 50. The calendars cost $4.50 each, and J&B sells them for $10 each. Suppose that J&B throws out all unsold calendars at the end of July. Using marginal economic analysis, how many calendars should be ordered? b. If J&B sells any surplus calendars for $1 at the end of July and can sell all of them at this price, how many calendars should be ordered?
Explanation / Answer
The purchasing price of a calendar = $4.5
The selling price = $10
Profit = $5.5
This Question can be done in Newspaper boy Model Problem, and
Newspaper boy Model = c1/(c1+c2)
Where C1 is the cost of Unsold = $10-$4.5 = $5.5 &
C2 = Purchasing price C2= $4.5
The newspaper boy Model = C1/(C1+C2) = 5.5/(5.5+4.5) = 5.5/10 = 0.55
The probabilty = 0.55, the value of Z under Normal distribution when Z= 0.5 is 0.3.12 AND Z=0.05 is 0.13.
So the value of Z When probability =0.55 is 3.12+0.13= 3.25
In standard Normal distribution Z= (X-Mean)/SD
3.25 = (X-500)/50
3.25*50+500 = X
= 162.5+500 = 662.5 units
The optimum Qunatity to be purchased = 662.5
b) If the supluse calendars are sold at $1
Then the cost of Unsold = $10-$4.5-1 = $4.5
C2= 4.5
The newspaper boy model = c1/(c1+c2) =4.5/(4.5+4.5) = 0.5
The value of Z when probability = 0.5 is 3.12
Z=(X-Mean)/SD
3.12 = (X-500)/50
3.12*50+500 = x
660 Units
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