Firm A is a tech company that specialises in developing scientific instruments for various organisations. Firm A has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year for one of the Governments office. The bid must be sealed, so that no company knows what the others are bidding, and the lowest bid wins the contract. Firm A estimates that it will cost 5 million to prepare a bid and another 95 million to supply the instruments if it wins the contract. Hence, for example, if Firm A wins the bid with the bidding offer of 120 million, then its net profit will be 20 million (=120-95-5).

On the basis of the past contracts of this type, Firm A believes that the possible low bids from the competition, if there is any competition, and the associated probabilities are those shown below.

	Less than 115	Between 115 & 120	Between 120 & 125	Greater than 125
Prior Probability	0.2	0.4	0.3	0.1

Given the above information, Firm A has four strategies: Bid 115, Bid 120, Bid 125, No Bid. In addition, Firm A believes there is a 30% chance that there will be no competing bids. Develop a decision tree model that finds the EMV for various bidding strategies. Find an optimal bidding strategy that maximises Firm As EMV.

1. Draw a decision tree that represents the above problem. Clearly indicate all necessary information according to the standard notion introduced in class. For example, use square and circle to indicate the decision and chance nodes, respectively. In addition, write down the corresponding probability and the associated EMVs next to each branch, whenever applicable.

2. Solve the problem by using the decision tree constructed in part (a). Clearly indicate the optimal solution and the resulting outcome. For calculations, feel free to use excel.