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Assignment Solutions for Business 2400

(i) For general instructions about assignments, please see Section 3 of the Course Out-line, especially Section 3.3 on file formats.

(ii) This document has been created only for internal use at Memorial University. This pdf file is not to be forwarded to anyone not currently registered in Business 2400.

Any transmission of the solutions to this assignment to a third party constitutes academic dishonesty.

(iii) For the problems which require Bayesian revision, please use five decimal place accuracy. You may use either tables done by hand, or tables done in Excel, or probability trees.

1. A company has developed a new type of mosquito repellant. The technical success is clear, but as with any new product the commercial success is risky.

Because of this, they would sometimes test-market a product first, and then make adecision about national marketing after the test-market results had come in; at other times they would proceed directly to national marketing. On some occasions, they would abandon the product without even test-marketing it.

The test-marketing would cost about $600,000. If successful (probability 0.4)there would be revenues of $200,000; if unsuccessful the revenues would only be $50,000. Should the test market be successful, a followup national campaign at a cost of $2,500,000 would have a 70% chance of success with a revenue of $9,000,000, otherwise it would be a failure with a revenue of $750,000. Should the test market be unsuccessful, a followup national campaign would have only a 0.2 chance of success (with the same cost, and the same revenues for success and

failure).

A national campaign not preceded by a test campaign would have a 45% chance of success. It would cost $3,000,000, and would produce a revenue of $9,500,000 if successful, but only $875,000 otherwise.

(a) Draw and solve a decision tree for the situation (using payoff nodes where appropriate), and state the recommendation clearly.

(b) If the $3,000,000 figure in the last paragraph were changed to $4,000,000, what would be the revised recommendation? Business 2400, Fall 2021, written by Dr. David M. Tulett 2

2. (20 marks) A farming couple have been in the habit of always planting onions on their farm. In previous years, the seeds for the onions were planted in the spring, and were ready to harvest in mid-July. After that, a second planting took place in late July, which was ready to harvest in early October.

This year, however, there is concern that insects might destroy some or all of the onion crop. One thing they could do would be to plant a different crop such as carrots which would not be affected by the insects. The carrots would have only a single planting at a cost of $80,000. This planting would yield a crop in October worth $140,000 if the weather turns out to be good, or $60,000 if the weather turns out to be poor. There is a 70% chance that the weather will be good.

If, however, they decide to plant onions, they will have to worry about the insects (but the weather has little effect on the onion crop and can be ignored). The onion crop would cost $100,000 to plant. There is a 10% chance of a severe infestation of insects, which would destroy the crop, and render any attempt at a second planting in late July not worth doing. A mild infestation (30% chance) would partially de-stroy the crop, making it worth only $70,000, while having no insects (60% chance) would produce a crop worth $160,000. After either a mild infestation or no infestation, a second planting could be undertaken, with the same costs and revenues as the first. The probability of a severe, mild, or no infestation would be 25%, 35%, and 40% if the first planting had a mild infestation, but would be 5%, 10%, and 85% if the first planting had no infestation.

Draw the tree, solve it using the rollback procedure, and state the recommendation and the ranking payoff. When drawing the tree, use payoff nodes for intermediate payoffs. Business 2400, Fall 2021, written by Dr. David M. Tulett 3

3. (18 marks) A company has identified a potential new type of cereal which would require $900,000 in start-up costs to launch. If it turns out to be a major success, there will be a $5,000,000 contribution to profit. A minor success would give a profit contribution of $1,000,000, while a failure would have a profit contribution of only $250,000. The company is most worried about this third possibility, since in this case the net profit would be $250,000 minus $900,000, i.e. a loss of $650,000. In the past, one new product in twenty became a major success, one new product in five became a minor success, and the other three-quarters of them became failures; there is no reason to suspect that this product would be any different from the rest. Some of their competitors use an outside independent market research firm to give them advice about new products. The fee for the research firm is $25,000; in return, the consumer products company would be told that the proposed product either “looks well” or “looks poorly”. The research company had established a track record which gave them confidence about saying the following:

(a) If a product would be a major success, they would say “looks well” with probability 0.8;

(b) If a product would be a minor success, they would say “looks poorly” withprobability 0.7;

(c) If a product would be a failure, they would say “looks poorly” with probability0.9.

Develop a decision tree and solve it to obtain a recommendation.

4. (18 marks) It is known that oil exists beneath the surface at a particular location,but it is not known if it’s just a small pool of oil (this has a 90% probability), or if there’s a large pool of oil. A small pool is worth only $500,000, but a large pool would be worth $12 million. To drill (which will determine the size of the pool) would cost $2,000,000. If they do not drill, an $80,000 environmental inspectiofee will be refunded to them.

A seismic test is available at a cost of $45,000; the result will be either “positive” or “negative”. If a large pool of oil is present then there’s an 80% chance of a positive result; if there’s just a small pool present then there’s a 30% chance of a positive result.

Draw and solve a decision tree to determine a recommendation for this situation. Business 2400, Fall 2021, written by Dr. David M. Tulett 4

5. (24 marks) There’s a 10% chance that pirates in the 17th century buried their treasure (bars of silver and gold) about 35 to 40 metres beneath the surface at a particular location. If so, it would be worth about $8,000,000 at today’s prices. Otherwise,

there’s a 90% chance that there’s no treasure. To dig to a depth of 40 metres (which would be enough to either find the treasure, or conclude that there’s no treasure at this location) would cost $750,000.

A test based on magnetism is available at a cost of $25,000; the result will be either “positive”, “inconclusive”, or “negative”. If the treasure is present then there’s a 70% chance of a positive result; a 16% chance of an inconclusive result, and a 14% chance of a negative result. If the treasure is not present these percentages become 10%, 26%, and 64% respectively. The company has decided that if they do a magnetism test and if it turns out to be negative, then they will not dig for treasure.

There’s also a second test available. This could only be used after doing a magnetism test and obtaining an inconclusive result, and if used would cost $15,000. If there’s treasure present the second test will report “favourable” with probability 0.8; if there’s no treasure the second test will report “unfavourable” with probability 0.85. If an “unfavourable” result is obtained then they will not dig for treasure. Draw a decision tree and solve it using the rollback procedure to determine a recommendation for this situation. (In doing the Bayesian revisions you do not need to calculate any probabilities which are not needed for the decision tree).