För a two-person zero-sum game between players X and Y, the payoff matrix for X is: Y1 Y2 X1 1. 3. X2 4. X3 Formulate the linear program for finding the best mixed strategy for X that maximizes its minimum expected payoff, EP, with p1, p2, and p3 being the respective probabilities for playing strategies X1, X2, and X3 (5 points deducted for any incorrect or missing element of the formulation).
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- The table below states the payoffs in profits (of millions of tenge each day) to two grocery supermarkets that are rivals in Almaty, Blue Foods and Ladymart. Each supermarket can take one of two courses: Low prices; or high prices. In each cell, the first payoff is for Blue Foods, and the second payoff is for Ladymart. (a) Assume that neither store observes the pricing by the other store, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total profits to the two stores? (b) Now assume that each store can observe the pricing by the other store, and solve the game. Blue Food, Ladymart High prices Low prices High prices 2, 2 0, 3 Low prices 3, 0 1,1The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day Store 1 Store 2 1 889 2 Difference (Store 1 - Store 2) Send data to calculator V 3 699 534 479 525 252 4 398 5 432 364 160 6 7 8 213 252 929 32 234 632 410 174 282 34 272 181 18 297 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μ (which is u with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally…The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day Store 1 Store 2 1 467 Difference (Store 1 - Store 2) Send data to calculator V 361 Explanation Check 106 2 865 903 - 38 3 254 4 704 5 929 102 611 671 6 418 550 7 (a) State the null hypothesis H and the alternative hypothesis H₁. Ho : D 734 737 152 93 258 - 132 -3 8 621 690 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is u with a letter "d" subscript), the population mean daily sales difference between the…
- A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 25% chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy 40% of the crop and reduce the profit to $60,000. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $5000. Should the grower spend the $5000 and thereby reducethe profit to $95,000? [Hint: Compute E(X ), where X is theprofit the grower will get if he does nothing to protect the fruit.]Find the value of the game given the payoff matrix below and the optimal mixing strategies of both players.. The table below states the payoffs in political points (measured in billions of rubles) to two nations that are rivals in world politics, Russia and Ukraine. Each country can take one of two courses: peace; or war. In each cell, the first payoff is for Russia, and the second payoff is for Ukraine. (a) Assume that neither country observes the military strategy of its rival, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total political points? (b) In general, what is a Nash equilibrium? Is the solution to this game a Nash equilibrium? (c) Suppose that each country deposits a fund of two billion rubles with the United Nations. Either country would forfeit this fund if it wages war. What is the solution now to the game? Is this a Nash equilibrium? Russia, Ukraine Peace War Peace 4,4 1, 5 War 5, 1 2,2
- FRQ #2: A certain company makes three grades (A, B, and C) of a particular electrical component. Historically, grade A components have a 2 percent defective rate, grade B components have a 5 percent defective rate, and grade C components have a 10 percent defective rate. Since grade A components are less likely to be defective, the company can charge more money for those components than it can charge for the grade B or C components. Similarly, the company can charge more money for grade B components than it can charge for grade C components. Recently, the company found a batch of components in a warehouse that were known to be of the same grade, but the grade was not labeled on the components. To determine the grade (A, B, or C), the company selected from that batch a random sample of 200 components, which contained 16 defective components. a) Construct and interpret a 95 percent confidence interval for the proportion of defective components in the batch. b)Does the interval calculated…Reduce the payoff matrix by dominance.Morris’s kidneys have failed and he is awaiting a kidney transplant. His doctor gives him this information for patients in his condition. Of those patients who get matched with a kidney, 90% survey the transplant operation and 10% do not. The transplant succeeds in 60% of those who survive and the other 40% must return to kidney dialysis. The proportions of those who survive for at least 5 years post transplant is 70% for those who had a successful transplant and 50% for those who return to dialysis. Assuming Morris is matched with a kidney, what is his chance of surviving 5 years post transplant. It may be helpful to draw a tree diagram to solve this problem.
- A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r 5 P(#2 fails | #1 fails). P(#2 fails) = q. If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?A venture capitalist, willing to invest $1,000,000, has three investments to choose from: The first investment, a software company, has a 10 percent chance of returning $5,000,000 profit, a 30 percent chance of returning $1,000,000 profit, and a 60 percent chance of losing the million dollars. The second company, a hardware company, has a 20 percent chance of returning $3,000,000 profit, a 40 percent chance of returning $1,000,000 profit, and a 40 percent chance of losing the million dollars. The third company, a biotech firm , has a 10 percent chance of returning $6,000,000 profit, a 70 percent of no profit or loss, and a 20 percent chance of losing the million dollars. Find the expected value for each investment. The software company's expected value is $__ The hardware company's expected value is $___ The biotech firm's expected value is $___ Which investment has the highest expected return, on average? (software, hardware or biotech)Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the time while C uses the minimax strategy 50% of the time and chooses each of the other two columns 25% of the time. (Round your answer to two decimal places.)