# Practice Questions on Decision Tree

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1.Â Â Â Â Â Â Â Â  Represent the following decision making problem by a Decision Tree.

 Action S1 S2 S3 A1 200 420 – 120 A2 550 70 250 Probability 0.3 0.5 0.2

2.Â Â Â Â Â Â Â Â  As a byproduct of another research, the Excel Pharmacy has come across a substance which has potential of being developed as skin lotion.

A manor company in the consumer industry has offered to buy rights to the lotions for ` 5 lakhs. It would then attempt to develop the product itself.

Excel Pharmacy is still considering to develop the product itself. The development costs are estimated to be ` 7,50,000 and the product will have a 50 : 50 chance of being successful. It the product is successfully developed, several companies will try to buy the rights. Excel Pharmacy believes that there is 0.40 probabilities that it could receive ` 28 Lakhs for rights and 0.60 chance that it could receive ` 20 lakhs.

Another option after the successful development of the product for Excel Pharmacy could be to market the product itself. The possible returns for this option will be ` 10 Lakhs, ` 20 Lakhs and ` 48 Lakhs with the probabilities of 0.3, 0.5 and 0.2 respectively.

Later, if Excel Pharmacy is unsuccessful in its attempt to develop the product, it feels that it could still sell the rights but now only for ` 1,25,000.Â  Represents all courses of action and their economic consequence into decision tree and identify an optimal plan of action for the pharmacy.

3.Â Â Â Â Â Â Â Â  A firm has developed a new product X. They can either test the market or abandon the project. The details are set out below :

Test market cost ` 50,000 likely outcomes are favourable (P = 0.7) or failure (P = 0.3). If favourable, they could either abandon or produce it when demand is anticipated to be

 Low P = 0.25 Loss ` 100,000 Medium P = 0.60 Profit ` 150,000 High P = 0.15 Profit ` 450,000

If the test markets indicate failure, the product would be abandon. Abandonment at any stage result in a gain of ` 30,000 from the special machinery used.

(i)Â Â Â Â Â  Draw a decision tree showing the nodes and possibilities.

(ii)Â Â Â Â  Evaluate the decision tree.

4.Â Â Â Â Â Â Â Â  A cigarette Company is considering the introduction of a new filter cigarette brand. Each carton of the cigarette will contain 20 packs. The Company estimates that it will be able to sell 10,000 â€“ 20,000 cartons in a given period with probabilities given below :

 Numbers of cartons in (â€˜000) sold Probability 15 1 15 5 20 4

If the company launches the product, it will incur a fixed cost of ` 62,000. Each carton sold would fetch a contribution of ` 4. Should the Company introduce the new brand?

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