A company has to transport 1m live sheep. The company, however, faces a 50% chan

Question

A company has to transport 1m live sheep. The company, however, faces a 50% chance of losing all the sheep on any one trip, due to stress. The transport costs are borne by the consignee. The company is considering two strategies: i. Take the entire cargo in one trip ii. Take two trips with half the cargo in each trip a. List the possible outcomes of each strategy and the probabilities of these outcomes. b. One the average, how many sheep will remain alive at the end of the trip, under either strategy. c. Are there greater benefits from taking more trips? Will this be affected if the company has to bear the cost of transport?

Explanation / Answer

A)

Strategy 1:

Probability that no sheep will live = 0.5

Probability that all sheeps will live = 0.5

Strategy 2:

Probability that no sheeps will live = 0.5x0.5 = 0.25

Probability that half sheeps will live = 2 x 0.5x0.5 = 0.5

Probability that all sheeps will live = 0.5x0.5 = 0.25

B) under strategy 1, expected number of sheeps that will survive = 0x0.5 + 1x0.5 = 0.5 million

Under strategy 2, expected number of sheeps that will survive = 0x0.25 + 0.5x0.5 + 1x 0.25

= 0.5 million

C) There are no benefits in taking more trips. If the company have to bear the transportation cost, it is preferable to transport the sheeps in a single trip

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