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muthudivyaj says

Dear Tutor,

This is with regard to the probability values used in question b(i) expected value of example 1 in chapter 7 (Risk and Uncertainity, P5 Opentuition Course notes).

In the calculation of the expected values for the above example, we know that in some cases the demand cannot be met due to limited capacity. With a given maximum capacity of 1200 units, our fixed contract units and demand must be equal or less than 1200 units.

Therefore, with a fixed contract of 800 units, a demand of 400 units can only be met. Other levels of demand cannot be met as it exceeds the capacity.

Similarly, with a fixed contract of 700, a demand of 700 (i.e 700+700=1400 > 1200) and demand 900 units can not be met; and with a fixed contract of 500 units, a demand of 900 units cannot be met.

1) How is the expected value of 4,400 been arrived at (with fixed contract of 800 units and demand of 400 units) given the probability in the question is 0.2 for a demand of 400 units ? Should the expected value not be 880 (i.e 4400 x 0.2) instead of 4,400 (4,400 x 1). If the probability is taken as 1, would it not mean that the outcome is certain?

2) Similarly in the case of a fixed contract of 700 units, the probability of 500 units of demand is taken as 0.8 when the question clearly states 0.3. Can you please explain how the probability can be changed (when the levels of demand are not met due to limited capacity) though the question clearly gives the probability for the level of demand?

I look forward to your reply.

Thank you.

doubleminttwins says

Yes. Can the lecturer please clarify. As we are applying the probability to the demand not the contract. If we take the contract and thereby reducing our available supply to normal demand, what probability do we apply or does it not matter?

John Moffat says

My answer to the question above should answer your question

John Moffat says

1) Since the contribution will be 4400 whatever happens, the expected value is 4400!! If you prefer it with probabilities (although you really should not need to), it is as follows:

(0.2 x 4400) + (0.3 x 4400) + (0.4 x 4400) + (0.1 x 4400) = 4400

2) Of course the probability has not changed. Using the same logic as in (1) it is rather quicker to take 4,600 x 0.8 instead of (4600 x 0.3) + (4600 x 0.4) + (4600 x 0.1), which will give exactly the same answer. For the exam of course it does not matter – whichever you are more comfortable with, since it gives the same answer.

(One think that you might not realise (I cannot be sure from your question) is that if normal demand cannot be met in full, we at least assume that we sell to them what we can. The lecture does make this clear)

muthudivyaj says

Dear Mr. John Moffat,

Thank you for your prompt reply.

It has been made clear that:

1) Where the demand + fixed contract size = or than the maximum capacity, the enterprise will go on produce to its maximum capacity to meet as much of the demand as it can. Therefore, when the contract size is 800 and the demand is 900, the factory will go ahead to produce its maximum capacity less the fixed contract size i.e (1200 – 800 = 400).

Once again, thank you very much.