Question:

Mathematics: Simulation, Averages?

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A new monthly magazine called "Get Green" has come on the market.

A particular newsagent has places an order for 36 copies to be delivered to his shop monthly. He pays the publisher €3.20 per copy and sells the magazine for €5.10 per copy. Any copies unsold at the end of the month can be returned by the newsagent for a refund of €0.80. He will have to pay a penalty cost of €1.20 for each dissatisfied customer.

The demand for the magazine has the following probabilities:

Demand Per Month(Probability):

27(0.07), 30(0.23), 33(0.31), 36(0.23), 39(0.10), 42 (0.05), 45 (0.01)

Using the set of following set of random numbers:

22, 93, 09, 81, 47, 78, 17, 52, 81, 02

(i) Simulate 10 months demand of the magazine.

(ii) Calculate the average monthly profit or loss associated with the sale of the magazine.

(iii) Calculate the expected level of demand for the magazine.

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1 ANSWERS


  1. (i) ANSWER: 10 MONSTHS  DEMAND = 390

    Why??

    10 MONTHS DEMAND = 10 MONTHS * MONTHLY AVERAGE DEMAND = 10 * 39

    (ii) ANSWER: AVERAGE MONTHLY PROFIT     [€183.6 - €116.60 = €72.00]

    Why??

    AVERAGE MONTHLY PROFIT = MONTHLY AVERAGE DEMAND * PRICE - COSTS

    MONTLY AVERAGE DEMAND = Σx * P(X = x) = 39

    COSTS = 36[ORDERED COPIES] * €3.20 – 3[UNSATISIFED CUSTOMERS] * €1.20 = €116.60

    P(X = x) = PROBABILITY   [0.07, 0.23, 0.31, 0.23, 0.10, 0.05, 0.01]

    (iii) ANSWER: EXPECTED LEVEL (AVERAGE) MONTHLY DEMAND =  39

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