A newspaper boy purchases newspapers early in the morning and cannot repurchase on the same day. If he purchases the newspapers at ₹8 each and sells them at ₹12 each. If the newspaper remains unsold he can return it for ₹2 each. The customer goodwill loss is expected as₹ 1.5 each. What will be the optimum quantity to be purchased? The probability of newspaper sales per day is given in the table?

Demand Probability

10 0.44

15 0.05

20 0.13

25 0.26

30 0.31

35 0.09

40 0.09

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Solution

The correct option is D 25

$Potential profit, p = S_{p} - C + C_{_{b}}$

$S_{p} \to Selling price$

$C \to Purchasing cost/ unit$

$C_{b} \to Back ordering or goodwill lost/unit$

$p^{'} = 12 - 8 + 1.5$

$= ₹ 5.5$

$Loss per unit, l = C - C_{b} + C_{h}$

$C_{s} = Scrap value/unit$

$C_{h} = Holding cost/unit$

$l = 8 - 2 + 0$

$l = ₹ 6$

$p (S - 1) \leq \frac{p}{p + l} \leq p (s)$

$Now, \frac{p}{p + l} = \frac{5.5}{5.5 + 6} = 0.4783 = 47.83 %$

So, the optimum profit number of newspapers purchased is 25.

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