Question 36048: Hi Could somebody help me or give me guidance on how to answer the questions below please, thanks, Sarah
Sam's Takeaway has the opportunity to open a new shop, but is unsure of the demand. Initial estimations are that there is a 80% chance of high demand and 20% chance of low demand.
Sam's Takeaway must choose between a large, medium or small shop. The large shop has the potential to make a profit of £50,000 if there is high demand but a loss of £10,000 if demand is low. The medium shop could make £40,000 or £15,000 depending on whether there is high or low demand, respectively. Whilst, the small shop could yield a £20,000 profit with high demand or £10,000 with low demand.
1 (a) Sam will use the Expect Value Approach, with the probabilities above. Construct a table, in Microsoft Excel to compare the decision alternatives. This table should use formulas where appropriate, and be able to clearly show the “expected value” and also a description of the preferred shop size.
(6 marks)
(b) Sam's Takeaway revises their estimations from 80% high demand and 20% low demand to 70% high demand and 30% low demand Does this change to decision alternative, and if so how?
Answer by Prithwis(166)   (Show Source):
You can put this solution on YOUR website! Find the probabilities of each event, as specified in your question.
The probability of high demand for Sam to open a new shop is .80;
The probability of low demand for Sam to open a new shop is .20;
For Large Shop:
Potential profit on high demand is £50,000
Potential loss on low demand is £10,000
Expected value is determined as E = x1.p1 + x2.p2 + ... + xn.pn where xi is the value associated with i-th event and pi is the probability of i-th event.
E (for large shop) = (£50,000)(.8) + (-£10,000)(.2) (-ve value is due to loss)
=> E (for large shop) = £40,000 - £2000 = £38,000 (expected gain);
E (for medium shop) = (£40,000)(.8) + (£15,000)(.2)
=> E (for medium shop) = £32,000 + £3000 = £35,000 (expected gain);
E (for small shop) = (£20,000)(.8) + (£10,000)(.2)
=> E (for small shop) = £16,000 + £2000 = £18,000 (expected gain);
Preferred shop size would be large because it generates the maximum profit.
..........
You can use the same approach for the revised demand (probabilities will be different based on the revision; one will .7, instead of .8; the other will be .3, instead of .2)
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