The manager of the Hermon Ski resort must choose the operation strategy of the s

Question

The manager of the Hermon Ski resort must choose the operation strategy of the site for the coming year: to open up all ski trails or to open up just half Her decision depends on the weather forecast: if there is a large blizzard before the ski season, then all trails will be covered with enough snow; if there is only a small blizzard, then the resort will need to fire up their snow making machines to cover the ski trails. Using the snow making machines, of course, is costly. The manager estimates that the profits (in thousands) for each course of action are: Large Blizzard Small Blizzard 107 Open up all trails Open only half of the trails 87 20 54 After considering the weather forecast, the manager believes that the probability of a Large Blizzard is p, and that the probability of a Small Blizzard is 1-p. What is the minimal value that p (the probability of a Large Blizzard) must have so that Opening up all the trails is the best strategy for the manager? Round your answer to the nearest hundredth, i.e. if you get 0.45677 your answer should be 0.47

Explanation / Answer

Solution: Given the above information, expected profit by opening up all trails = p*107 + (1-p)*20

E(open all) = 107p + 20 - 20p = 87p + 20

And expected profit earned by opening only half the trails = p*87 + (1-p)*54

E(open half) = 87p + 54 - 54p = 33p + 54

Opening up all the trails is the best strategy for the manger, if E(open all) >= E(open half)

So, 87p + 20 >= 33p + 54

On solving this, 87p - 33p >= 54 - 20

54p > 34 or p >= 34/54 = 0.6296

So, for the minimal value of p = 0.63 (rounding to nearest hundredth), opening up all trails will be the best strategy for the manager.

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