A retailer is deciding how many units of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $11 per unit and sells for $25 per unit. What is the conditional value for the decision alternative "Stock 3" and state of nature "Sell 1"?
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A retailer is deciding how many units of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $11 per unit and sells for $25 per unit. What is the conditional value for the decision alternative "Stock 3" and state of nature "Sell 1"?
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- Jeffrey Mogul is a Hollywood film producer, and he is currently evaluating a script by a new screenwriter and director, Betty Jo Thurston. Jeffrey knows that the probability of a film by a new director being a success is about .10 and that the probability it will flop is .90. The studio accounting department estimates that if this film is a hit, it will make $25 million in profit, whereas if it is a box office failure, it will lose $8 million. Jeffrey would like to hire noted film critic Dick Roper to read the script and assess its chances of success. Roper is generally able to correctly predict a successful film 70% of the time and correctly predict an unsuccessful film 80% of the time. Roper wants a fee of $1 million. Determine whether Roper should be hired, the strategy Mogul should follow if Roper is hired, and the expected value.A firm must decide whether to construct a small, medium, or large stamping plant. A consultant’sreport indicates a .20 probability that demand will be low and an .80 probability that demand willbe high.If the firm builds a small facility and demand turns out to be low, the net present value will be$42 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $42 million or expand greatly for a net present value of $48 million.The firm could build a medium-size facility as a hedge: If demand turns out to be low, its netpresent value is estimated at $22 million; if demand turns out to be high, the firm could do nothingand realize a net present value of $46 million, or it could expand and realize a net present value of$50 million.If the firm builds a large facility and demand is low, the net present value will be – $20 million,whereas high demand will result in a net present value of $72 million.a. Analyze this problem using a decision…Swell Productions is sponsoring an outdoor conclave for owners of collectible and classic Fords. The concession stand in the T-Bird area will sell clothing such as T-shirts and official Thunderbird racing jerseys. Jerseys are purchased from Columbia Products for $40 each and are sold during the event for $75 each. If any jerseys are left over, they can be returned to Columbia for a refund of $30 each. Jersey sales depend on the weather, attendance, and other variables. The following table shows the probability of various sales quantities. How many jerseys should Swell Productions order from Columbia for this one-time event?Sales Quantity Probability Quantity Sales Probability100 0.05 400 0.34200 0.11 500 0.11300 0.34 600 0.05
- A firm must decide whether to construct a small, medium or large stamping plant. A consultant’s report indicates a 0.20 probability that demand will be low and 0.80 that demand will be high. If the firm builds a small facility and demand turns out to be low, the Net Present Value (NPV) willbe $42M. If demand turns out to be high, the firm can either subcontract and realize the NPV of $42M orexpand greatly for a Net Present Value of $48M. The firm could build a medium size facility as a hedge: if demand turns out to be low, its NPV is estimated at $22M; if demand turns out to be high, the firm could do nothing and realize a NPV of $46M, or could expand and realize a NPV of $50M. If the firm builds a large facility and demand is low, the NPV will be ($20M), whereas high demand will result in a NPV of $72M. Compute the EVPI *MegaJoy Corp. is planning to open a new video arcade. It has narrowed the choices to a large or small arcade.(All costs and revenues in this problem are expressed in thousands of dollars.) The cost of a large arcade is $400, and the cost of a small arcade is $300.It has forecast that the demand will be low with probability 0.3 and high with probability 0.7.If MegaJoy builds a small arcade and the demand is high, then it expects revenues of $540. If MegaJoy builds a large arcade and the demand is low, then it has two alternatives: do nothing and earn revenue of $380, or reduce prices and earn revenues of $450. a. Draw a decision tree for this problem. b. Which choice yields the maximum expected money value?( Show calculation) c. A consulting firm has offered to perform reseach and forecast the demand fo MegaJoy. The firm will charge $8(thouthand) for its services, and it claims that the information will be 100% accurate. Should MegaJoy pay for the consulting services? Justify your…Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 7 Medium complex, d2 14 5 Large complex, d3 20 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for…
- 1. Kirsten is trying to decide where to go for her well-earned vacation. She would like to camp, but if the weather is bad, she will have to go to a motel. Given the costs and probabilities of bad weather given below, which destination should she choose? Camping cost Motel cost Probability of bad weather Nevada $21.2 $80.9 0.2 Oregon $15.9 $84.6 0.4 California $30 $95 0.1 a. California, because its EMV = $33.14 b. Nevada, because its EMV = $33.14 c. California, because its EMV = $36.5 d. Any of the 3 choices. e. Oregon, because its EMV = $43.38 f. Nevada, because its EMV = $43.38 g. None of the 3 choices. h. Oregon, because its EMV is $36.50.The Hard to Beat Bakery is deciding whether to buy or repair an existing oven thatthey have been using for over 8 years. If they elect to repair, it will cost the entity$950,000 and either of two outcomes is likely: 1. A 20% probability it will perform okay and generate revenues of$10,000,000, or 2. An 80% chance that it will be partially restored and generate revenue of$2,000,000. If on the other hand however, they purchase a new oven, they can either buy animported oven for $3,500,000 or they can buy a locally made one for $2,200,000.If the elect to purchase the imported oven, production will earn them revenues of$15,550,000, but if they buy the locally made oven, there is a 70% likelihood thatit perform as expected and generate revenues of $12,000,000; and a 30% chancethat it will not and generate revenues of $6,000,000. Required: 1. Draw a decision tree of this problem and determine the expected value.2. Advise the management of the Bakery on how to proceed.3. Briefly discuss the…11. Bakery Products is considering the introduction of a new line of pastries. In order to produce the new line, the bakery is considering either a major or a minor renovation of its current plant. Bill Wicker, head of operations, has developed the following conditional values table: Alternatives Favorable Market Unfavorable Market Major renovation $100,000 -$90,000Minor renovation $40,000 -$20,000 Do nothing $0 $0 Assume that the probability of a favorable market is equal to the probability of an unfavorable market.Part 2a) Choose the appropriate decision tree showing payoffs and probabilities.A.MinorFavorable40,000Unfavorable-20,000UnfavorableFavorableMajor100,000-90,000Do…
- A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? What is the expected profit? b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows: Let H = High resistance to rezoning L = Low resistance to rezoning P(H) = 0.55 P(S1 | H) =…Downtown Health Clinic needs to order influenza vaccines for the next flu season. The Clinic charges its patients $15.00 per vaccination and each dose of vaccine costs the clinic $4.00 to purchase. The Center for Disease Control has a long standing policy of buying back unused vaccines for $1.00 per dose. The Clinic estimates the following probability distribution for the season’s demand:Demand Probability2,000 0.053,000 0.204,000 0.255,000 0.406,000 0.10a. How many vaccines should the Clinic order to maximize its expected profit?b. The Clinic is trying to determine if they should participate in a new Federal program in which the cost of each dose is reduced to $2.00. However, to participate in the program, they can charge no more than $10.00 per vaccine. On strictly a profit maximizing basis, should the Clinic agree to participate?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