Two opposing armies, Red and Blue, must each decide whether to attack or defend. These decisions are made without knowledge of the opposing army's decision. The payoff table, in terms of value of property gained or lost for the Red Army, appears below. Any gains for the Red Army are losses for the Blue Army. Blue Army Attack Defend Red Attack 30 50 Army Defend 40 a. What is the optimal mixed strategy for the Red Army? b. What is the optimal mixed strategy for the Blue Army?
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- Cachora Dynamics Corp (CDC) has designed a new integrated circuit that will allow it to enter, if it wishes, the microcomputer field. Otherwise, it can sell its rights for $15 million. If it chooses to build computers, the profitability of this project depends on the company's ability to market them during the first year. Two levels of sales are foreseen as two possible outcomes: selling 10,000 computers in case of low demand, but if it is successful it can sell up to 100,000 units (high demand). The cost of installing the production line is $6 million. The difference between the selling price and the variable cost of each computer is $600. a) Develop a formulation for decision analysis and use the non-probabilistic decision rules: Maximin and Minimax. b) Assume that the probability of high demand (p) is 50% and for low demand (1 - p) is 50%, apply the probabilistic criteria: Maximum expected value, Minimum loss of opportunity. c) Determine the VEIP. d) Carry out a sensitivity…Option 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 farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop, given the two possible results on the trade bill, is shown in the following payoff table: Trade Bill Crop Pass Fail Corn $35,000 $ 8,000 Peanuts 18,000 12,000 Soybeans 22,000 20,000 Determine the best crop to plant, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz e. Equal likelihood
- 10. An investor must decide between two alternative investments-stocks and bonds. The return for each investment, given two future economic conditions, is shown in the following payoff table: Economic Conditions Investment Good Bad Stocks $10,000 $-4,000 Bonds 7,000 2,000 What probability for each economic condition would make the investor indifferent to the choice between stocks and bonds?You have an option to build a new mall or remove it. A new mall will cost P500M as investment to build it or demolish/remove an old one which cost P150M. To build – 75% chance of high demand – profit is P75M and a 25% weak demand w/ a profit of P25M. To remove – 60% chance of high demand – profit of P50M and a 40& weak demand w/ a profit of P10M. If you are the CEO, should you build or remove it. What is the EVM of either option? Draw the design tree.A retailer must decide whether to build a small or a large facility at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small facility is built and demand proves to be high, the manager may choose not to expand (payoff = $223,000) or to expand (payoff = $270,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is $200,000. If a large facility is built and demand proves to be low, the choice is to do nothing ($40,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff is estimated to be only $20,000; the payoff grows to $220,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is $800,000.Draw a decision tree. Then analyze it to determine the…
- In the following scenarios, you will be given a product and an event. Determine If there will be an increase OR decrease in either the supply OR demand, what happens to the price of the product, and what happens to the quantity bought and sold. The first two are answered for you as examples. EXAMPLE! 1 New oil fields are discovered by new companies in Canada EX 1 ANSWER Supply increases, price decreases, quantities increase EXAMPLE! 2 Penguin merchandise. The Penguins play well and contend for a playoff spot. EX 2 ANSWER Demand increases, price increases, quantities decrease 1. Beef. The price of chicken suddenly drops. 2. Newly constructed houses. The price of lumber doubles. 3. The government places a 30% excise tax on alcohol. 4. Peanut butter cookies. The price of chocolate chip cookies increases. 5. Pepsi.…Johnson Chemicals is considering two options for itssupplier portfolio. Option 1 uses two local suppliers. Each has a “unique-event” risk of 5%, and the probability of a “super-event” that would disable both at the same time is estimated to be 1.5%. Option 2 uses two suppliers located in different countries.Each has a “unique-event” risk of 13%, and the probability of a “super-event” that would disable both at the same time is esti-mated to be 0.2%. a) What is the probability that both suppliers will be disruptedusing option 1?b) What is the probability that both suppliers will be disruptedusing option 2?c) Which option would provide the lowest risk of a total shutdown?A store owner must decide whether to build a small or a large facility at a new location. Demand at a location can be either small or large, which probabilities estimated to be 0.4 and 0.6, respectively. If small facility is built and demand proves to be high, the manager may choose not to expand (payoff=P235,000) or to expand (payoff=P275,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is P220,000. If a large facility is built and demand proves to be low, the choice is to do nothing (P60,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff grows to P230,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is P900,000.a.) Draw a decision tree.b.) Determine the expected payoff for each decision and event node.c.)…
- The following is a breakdown of supplying and installing a piece of equipment to a project owner, atthe time of contract: EGPCost of equipment 250,000Manpower (installation) 50,000Overhead and profits 70,000i – Calculate the price of supplying and installing the equipmentii – If the supply and installing of the equipment was delayed by the project owner, calculate theescalated price of works based on the FIDIC Red Book 1990 formula given:Updated cost of equipment 270,000 EGPBase price index of manpower 123.2Updated price index of manpower 144.9In the following scenarios, you will be given a product and an event. Determine If there will be an increase OR decrease in either the supply OR demand, what happens to the price of the product, and what happens to the quantity bought and sold. The first two are answered for you as examples. EXAMPLE 1. Oil. New oil fields are discovered by new companies in Canada EX 1 ANSWER Supply increases, price decreases, quantities increase EXAMPLE 2 Penguin merchandise. The Penguins play well and contend for a playoff spot. EX 2 ANSWER Demand increases, price increases, quantities decrease 1. Yankees tickets. The Yankees built a new stadium that has 10,000 fewer seats. 2. Spam (Inferior good) . People’s incomes increase. 3. Foreign cars. The government places an excise tax on all foreign cars produced in the U.S. 4. Jelly.…The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company’s equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table: Material Costs Decision Stable Increase Houses $70,000 $30,000 Shopping center 105,000 20,000 Leasing 40,000 40,000 Determine the best decision, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz e. Equal likelihood