1. The Yellow Cab Pizza wants to launch a new pizza variant next month. After deliberations with their research department, marketing, finance and operations, they have broken down the possible variants into two (2) options: the Neapolitan and Chicago Deep Dish. The table below shows the possible profits (expressed in millions) for each option and the corresponding probabilities: Neapolitan Profit (x) Chicago deep dish Profit (xi) Probability (P,) Probability (P) 35 0.15 35 0.20 45 0.30 45 0.35 50 0.35 50 0.30 60 0.20 60 0.15
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- Payoff Table Decision Alternatives Demand Low Medium High Small, d1 400 500 600 Medium, d2 100 600 800 Large, d3 -300 400 1200 1). If nothing is known about the demand probabilities, what are the recommended decision using the Maximax (optimistic), Maximin (pessimistic) and Equally Likely? 2). If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45. What is the recommended decision using the expected monetary value approach? 3). What is the expected value of perfect information (EVPI)?A. A company wants to produce a souvenir with a marketing life of six months. Uncertainty surrounds the likely sales volume as well as the fixed costs of the venture as shown below: Sales units Probability Contrn. /unit Probability Fixed cost K7 K5 100 000 0.3 80 000 0.6 60 000 0.1 1.0 0.5 0.5 1.0 Determine the expected value of the contribution K400 000 K450 000 K500 000 Probability 0.2 0.5 0.3 1.02. A real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has two acceptable alternatives: residential proposal or commercial proposal. The main factor or state of nature that will influence the profitability of the development is whether or not a shopping center is built close by and the size of the shopping center. There is a 20% chance of no center being built, a 50% chance of a medium shopping center built, and a 30% chance of a large shopping center. If the developer selects the residential proposal and no center is built, he has a further set of options: do nothing $400,000 payoff; build a small shopping center himself $700,000 payoff; or put in a park resulting in $800,000 payoff. Should a medium shopping center be built nearby, his payoff for residential would be $1,600,000 and large shopping center results in a $1,200,000 payoff. If the developer selects the commercial proposal and no center is…
- A company wants to produce a souvenir with a marketing life of sixmonths. Uncertainty surrounds the likely sales volume as well as thefixed costs of the venture as shown below:Sales units Probability Contrn. /unit Probability Fixed cost Probability100 000 0.3 K 7 0.5 K400 000 0.2 Page 5 of 80 000 0.6 K 5 0.5 K450 000 0.560 000 0.1 K500 000 0.31.0 1.0 1.0 Determine the expected value of the contributionOption 2: Raise prices by 50%. If this occurs, there is a 75% chance that an Entrepreneur will set up in competition this year. The board’s estimate of its annual profit in this situation would be as follows: 2A: With new competitor 2B: Without new competitor Probability Profit (Sh.) Probability Profit (Sh.) 0.25 150,000 0.5 200,000 0.5 120,000 0.3 150,000 0.25 80,000 0.2 100,000 Option 3: Expand the car park quickly at a cost of Sh. 50,000 keeping prices theSame. The profits are then estimated to be like 2B above, except that the probabilities would be 0.6, 0.3 and 0.1 respectively. Required: Draw a decision tree for the above problem, including all the relevant data. Using expected values analyze the decision tree and recommend the best option to the owners of the car park.A well-known plastic mould and die manufacturer in Toronto intends to expand internationally in anticipation of strong demand and expansion in the plastic die manufacturing sector. use the table beneath. Using the Maximax, Maximin, and equally likely conditions, assist the business in making the best option in an unclear situation. 0.5 for a highly favourable condition, 0.2 for an average demand, and 0.3 for an unfavourable state are the probabilities linked with the states of nature.a) Choose the course of action that will give Andrew the highest predicted monetary value (EMV).b) Determine the anticipated value of perfect information (EVPI).
- 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…A decision maker has prepared the following payoff table. States of Nature Alternative High Low Buy 75 -10 Rent 70 30 Lease 50 35 Prior Probability 0.5 0.5 Using Baye's Decision Rule, what is the best decision and the expected payoff? (Round your answer to 1 decimal place.) Best decision РayofA decision maker has prepared the following payoff table. States of Nature Alternative High Low Buy 90 10 Rent 60 35 Lease 50 40 Using the Maximax criterion, what is the best decision and the expected payoff? Best decision Payoff 3 of 5
- DAAPS A decision maker has prepared the following payoff table. 1 States of Nature Alternative High Low Buy 80 10 Rent 60 45 Lease 50 40 Using the Maximin criterion, what is the best decision and the expected payoff? Best decision Payoff3. A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms that can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below. Wind-up action Pneumatic action Electronic action Demand Light Moderate $250,000 $90,000 -$100,000 400,000 440,000 400,000 Heavy 650,000 740,000 780,000 Construct the appropriate decision tree to analyze this problem. Use standard symbols for the tree. Analyze the tree to select the optimal decision for the manufacturer.A payoff table is given as: S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 (a) What choice should be made by the optimistic decision maker? (b) What choice should be made by the conservative decision maker? (c) What decision should be made under minimal regret? (d) If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?