December 1998
QT211: QUANTITATIVE ANALYSIS FOR MANAGEMENT

QUESTION 2

Total Marks: 20 Marks

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for Question 2

 
A baker's shop wishes to decide how many cream cakes it should make each day. Each cream cake costs $1 to make and sells for $2.50. Cakes are made in batches of 10, so the shopkeeper wants to use simulation to decide whether to make 50 or 60 cakes per day. If any cream cakes are left over at the end of the day, they are thrown away. Based on experience with other cakes, the shopkeeper believes that the estimated numbers of new customers on each day are expected to follow the probabillity distribution given below:

 

# new customers Probability
20 0.10
40 0.22
60 0.28
80 0.24
100 0.16

Each customer buys one cake each. If the shop sells all of its cakes on a particular day, then only half of the customers who arrive subsequently and are unable to buy a cake will return the following day, the other half will not return at all.

 
(a) Explain carefully how the above probability distribution can be used with the following sequence of random digits to simulate the number of new customers who wish to buy cakes each day over a ten-day period.

48   23    12   62   06   76   08   54    17   86

 

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(b) Determine on each day
  • how many new customers buy cakes
  • how many of the previous days customers return to buy cakes
  • the total number of customers who buy cakes
  • the total number of cakes that are wasted on each day

for each of the following

(i) if the shopkeeper bakes 50 cakes per day
(ii) if the shopkeeper bakes 60 cakes per day

 

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(c) How many cakes should the shopkeeper bake?

Note: 'new customers' are those who are attempting to buy a cake for the first time on a particular day. 'Previous days customers' are those customers who return to the shop because they are unable to buy a cake on the previous day because the shop had sold out of cakes.

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