White Valley Ski Resort is planning the ski lift operation for its new ski resort. Management is trying to determine whether one or two lifts will be necessary each lift can accommodate 250 people per day. Skiing normally occurs in the 14-week period from December to April, during which the lift will operate 7 days per week. The first lift will operate 90 percent capacity if economic conditions are bad, the probability of which is believed to be about a 0.3. During normal times the first lift will be utilized at 100 percent capacity, and the excess crowd will provide 50 percent utilization of the second lift. The probability of normal times is 0.5. If times are really good, the probability is 0.2., the utilization of the second lift will increase to 90 percent. The equivalent annual cost of installing a new lift, recognizing the time value of money and lift’s economic life is $50,000. The annual cost of installing two lifts is $90,000 if purchased at same time. Each lift costs $200,000 to operate, no matter how low or high its utilization rate. Lift tickets cost $20 per customer per day. (a)Should one or two lifts be purchased? (b)What is the Expected Value of Perfect Information?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
White Valley Ski Resort is planning the ski lift operation for its new ski resort. Management is trying to determine whether one or two lifts will be necessary each lift can accommodate 250 people per day.
Skiing normally occurs in the 14-week period from December to April, during which the lift will operate 7 days per week.
The first lift will operate 90 percent capacity if economic conditions are bad, the
During normal times the first lift will be utilized at 100 percent capacity, and the excess crowd will provide 50 percent utilization of the second lift. The probability of normal times is 0.5.
If times are really good, the probability is 0.2., the utilization of the second lift will increase to 90 percent.
The equivalent annual cost of installing a new lift, recognizing the time value of money and lift’s economic life is $50,000.
The annual cost of installing two lifts is $90,000 if purchased at same time. Each lift costs $200,000 to operate, no matter how low or high its utilization rate.
Lift tickets cost $20 per customer per day.
(a)Should one or two lifts be purchased?
(b)What is the
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