The Business Manager of Omaya Art Gallery has rented a hall to display the artworks of the artists of the gallery. She is considering organizing an exhibition of a number of rare painting masterpieces. In the past, only 70% of the paintings were sold in the first week. Moreover, if no painting is sold in the first five (5) days, the exhibition could be extended for another two (2) days but only 20% of the paintings would be sold.
The cost of the exhibition is GH¢500 per day. The manager estimated that in case she does not make any sales she will have to pay GH¢15,000 to cover the costs of renting the exhibition hall for the same period.
Required:
a) Draw a decision tree representing the Business Manager’s decision making process.                                                   (8 marks)

b) Calculate the expected monetary cost of each decision node.                                                                                        (6 marks)

c) Determine the Business Manager’s optimal strategy.                                                                                                     (6 marks)

Explain the following terms in decision making:
(i) Maximax Rule.                                                                                                                                                   (1 Mark)

(ii) Maximin Rule.                                                                                                                                                   (1 Mark)

(iii) Expected Monetary Value.                                                                                                                                (1 Mark)

(iv) Payoff table.                                                                                                                                                       (1 Mark)

(v) Expected value of perfect information.                                                                                                               (1 Mark)

Jodoo Company Ltd had a new, large order for its product and thinks that this may herald an expansion of the market, and therefore its sales and profits. The Jodoo Ltd could move the factory to a new and larger site which would ensure any future expansion needs were met, and this would cost GHS 1 Million. The existing factory could be expanded at a cost of GHS 0.25 Million, but this would limit the potential to meet particularly high increases in future market growth. Finally the new order could be met by overtime working at a cost of GHS 0.08 Million. Future increases in potential sales could only be partially met by this method. Consultants suggest that there are three likely scenarios, a 40 per cent increase in sales, a 10 per cent increase in sales and a 0 per cent increase in sales, with probabilities of 0.2, 0.6 and 0.2 respectively. A new factory would easily cope with increased sales and the likely extra profit from the 40 per cent sales increase would be GHS 6 Millions, whereas the expanded factory would have more problems in such a large expansion and would only yield extra profits of GHS 3.5 Millions, whilst overtime working would be able to make only modest increase in production, thus restricting extra profit to GHS 1.5 Million. If potential sales grew by 10 per cent, then a new factory would yield GHS 2.5 Million extra profit, and an expanded factory GHS 2.5 Million extra profit and overtime working GHS 1.5 Million Profit. A 0 per cent increase in potential sales would lead to a zero increase in profit under any of the options.
Required:
(i) Construct a decision tree to represent the varies scenarios of expansion.                                                                      (6 Marks)

(ii) Calculate the expected monetary value of each node of your tree in (i).                                                                      (8 Marks)

(iii) Advise the company on how to react to this opportunity.                                                                                            (6 Marks)