Harley, an ice-cream vendor, purchases each pint of ice-cream for $7 and sells for $20 each. At the end of the week, the unsold ice-cream can be salvaged for $2 each. From past experience, Harley has estimated the sales probabilities as below. What is the optimal number of pints Harley should purchase? Number of Ice-creams Sold, Probability 1 = 0.05, 2 = 0.1, 3 = 0.2 , 4 = 0.25, 5 = 0.15, 6 = 0.1, 7 = 0.08, 8 = 0.07

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A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000    Construct a decision tree to help the farmer make his decision. What should he do? Explain your answer.      Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop.     Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of…

GreenLeaf Electronics offers a new gadget that has been gaining popularity. The probability distribution for the number of gadgets sold per day is provided below. Calculate the average number of gadgets sold per day and determine the variance. NUMBER OF GADGETS SOLD    PROBABILITY100                                                      0.10200                                                            0.15300                                                             0.25400                                                             0.25500                                                            0.20600                                                            0.05

An oil company must decide whether or not to drill an oil well in a particular area that they already own. The decision maker (DM) believes that the area could be dry, reasonably good or a bonanza. See data in the table which shows the gross revenues for the oil well that is found. Decision Drill $0 Abandon $0 Probability 0.3 Dry (D) Seismic Results No structure(N) Open(0) Closed (C) Drilling costs 40M. The company can take a series of seismic soundings (at a cost of 12M) to determine the underlying geological structure. The results will be either "no structure", "open structure or "closed structure". The reliability of the testing company is as follows that is, this reflects their historical performance. Reasonably good(G) $85 $0 0.3 Note that if the test result is "no structure" the company can sell the land to a developer for 50 m. otherwise (for the other results) it can abandon the drilling idea at no benefit to itself. Dry(d) 0.7 0.2 Bonanza(B) 0.1 $200 m SO 0.4 Conditional…

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The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):     State of Nature   Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70   The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30.   Use a decision tree to recommend a decision.Recommended decision:    Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.   EVPI: $  fill in the blank 3 A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F | s1) = 0.10   P(U | s1) = 0.90 P(F | s2) = 0.40   P(U |…

Howard Weiss, Inc., is considering building a sensitive new radiation scanning device. His managers believe that there is a probability of 0.40 that the ATR Co. will come out with a competitive product. If Weiss adds an assembly line for the product and ATR Co. does not follow with a competitive product, Weiss's expected profit is $40,000; if Weiss adds an assembly line and ATR follows suit, Weiss still expects $20,000 profit. If Weiss adds a new plant addition and ATR does not produce a competitive product, Weiss expects a profit of $600,000; if ATR does compete for this market, Weiss expects a loss of $100,000. a) Expected value for the Add Assembly Line option = $ (enter your answer as a whole number).

The Astana airline always books more passengers on a flight than its capacity because of last minutes cancellations. The airline charges $835 per passenger from Almaty (Kazakhstan) to Frankfurt (Germany).  However, due to overbooking, it asks a few passengers travelling more than the plane’s capacity to take another flight and offers a coupon of $350, including hotel, meal, etc.  The experience has shown the following probability distribution corresponding to no-shows: Number of no-shows Probabillity 0 0.05 1 0.08 2 0.12 3 0.19 4 0.25 5 0.15 6 0.11 7 0.05 The airline hires you as a consultant because you have taken a course in supply chain management. What is the average number of no-shows based on the above distribution? How many overbookings should be made to minimize loss due to no shows, given the above probability distribution? Suppose you find out that last minute no-shows are normally distributed with a mean as determined in (a) above and a standard…