Section II: Cal culations (Write your answers in the space provided) Q1 (16%) Co

Question

Section II: Cal culations (Write your answers in the space provided) Q1 (16%) Consider a boy selling newspapers. The selling price eiven its wholesale price is $2. Suppose the demand distribution with for newspapers follows a normal an average of 1,000 and a standard deviation of 400. 4%) a) What is the marginal profit and marginal cost of an additional newspaper? ould the optimal quantity be equal to, smaller than, or larger than the average demand? Please explain why. (496) (b) Sh c) What is the optimal quantity that maximizes the boy's total expected profit? (8%) Critical ratio 0.5 0.65 0.67 0.68 0.7 z value 0.39 0.44 0.47 0.52

Explanation / Answer

Here mean demand = 1000

Standard deviation of demand   = 400

Selling price= $ 6

Buying price = $ 2

Salvage price = $0

so he has purchased Y newspapers on wholsale. his profit would be

Total profit = (6-2)Y = 4Y if X >= Y

= 4 X - 2 (Y-X) =6X - 2Y if X <= Y

here X is the demand varaible which follow ~ N(1000, 400)

(a) Marginal Profit of an addiational newspaper = $4

Marginal COst of an additional newspape= $ 2

(b) Here optimal quantity shall be higher than the mean deman of 1000. It is because the difference between Selling price and wholesale price ($ 6 - $ 2 = $4) is higher than the difference between wholsesale price and salvege parice ($2 - $0 = $2).

(c) Here Value of Z = (Selling price - Wholesale price)/ (selling price - salvage price) = (6-2)/(6-0) = 4/6 = 2/3 = 0.67

so Z - value for critical ration 0.67 is Z = 0.44

so Z = (X0 -)/

0.44 = (X - 1000)/ 400

X = 1000 + 400 * 0.44 = 1176 units

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