Question 1 -
A manufacturing company can produce a particular electrical device at a cost of RMIS. Each device for 'which there is demand in the week of production can be sold for RM80. However, due to the half-life of the components in the electrical devices, all devices that are not sold in the week of production need to be scrapped at a curt of RM10 per device. The weekly demand of the electrical device is given in the following table:
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|
Weekly Demand
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Number of units
|
0
|
60
|
120
|
250
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Probability of demand
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0.2
|
0.45
|
0.3
|
0.05
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How many devices should be produced per week to maximise the weekly mean profit of the company?
Question 2 -
The premium machine used by a company is at the end of its lifetime. The remaining operational lifetime of the machine is either 2 or 3 years with probability of ½. A decision must be made on how many spare pans of a certain component to produce. The demand for spare parts of the component follows a Poisson distribution with an expected value of I units per year for each year of the remaining lifetime of the machine. Assume that the demands in the various years are independent of each other and it is decided to produce W units of the spare part.
(a) Let Y denote the total demand for spare parts in the remaining operational lifetime of the machine, determine the probability mass function of Y.
(b) The value of the number of units left over at the end of the operational lifetime of the machine is given by
Determine E[f(Y)].
(c) Show that the expected value of the shortage is Sλ/2 - W + E[f(Y)].
(d) If the average demand is 5 units per year, what is the minimum number of spare parts that should be produced so that the probability that the production size will not be enough to cover the demand in the remaining lifetime of the machine is less than 5%?