Campaign Strategies27 Florida and Ohio are “swing states” that have a large bounty of electoral votes and are therefore highly valued by presidential campaign strategists. Suppose that it is now the weekend before Election Day 2012, and each candidate (Romney and Obama) can visit only one more state. Further, to win the election, Romney needs to win both of these states. Currently, Romney has a 40% chance of winning Ohio and a 60% chance of winning Florida. Therefore, he has a
a. Set up a payoff matrix with Romney as the row player and Obama as the column player, where the payoff for a specific set of circumstances is the probability (expressed as a percentage) that Romney will win both states.
b. Where should each candidate visit under the circumstances?
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Chapter 5 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
- Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 70% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 55% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 20% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 35% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson Robinson P = City Is the game strictly determined? Yes No Q= Rural City (b) Find the optimal strategy for both Robinson (row) and Carson (column). Ruralarrow_forwardA company manufactures shoes in three different factories. Factory Omaha Produces 25% of the company's shoes, Factory Chicago produces 60%, and factory Seattle produces 15%. One percent of the shoes produced in Omaha are mislabeled, 0.5 % of the Chicago shoes are mislabeled, and 2% of the Seattle shoes are mislabeled. If you purchase one pair of shoes manufactured by this company and you determine they are mislabeled what is the probability they were made in Omaha?arrow_forwardBella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 40% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson CityRural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =arrow_forward
- A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey? fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method.arrow_forwardThree FM radio stations (A, B, and C) are competing for customers in the same market area. Through an aggressive advertising campaign, each month station A is capturing 7% of station B's customers and 5% of station C's customers. (Hint: The phrase "station A is capturing 7% of station B's customers" means that 7% of the listeners are moving from B to A, not the other way around.) At the same time, station A is losing only 2% of its customers to B and 2% of its customers to C. Additionally, each month 1% of B's customers switch to C, and 1% of C's customers switch to B. Initially, A and B each have 30% of the listeners and C has 40%. Use this information to answer the following questions. (Give your answers correct to three decimal places. Note that you are asked to give decimal values and not percentages. For example, you would need to enter 0.628 as opposed to 62.800%.) (a) What fraction of the listeners will A have after 3 months? .900 (b) What fraction of the listeners willB have…arrow_forwardThree FM radio stations (A, B, and C) are competing for customers in the same market area. Through an aggressive advertising campaign, each month station A is capturing 7% of station B's customers and 5% of station C's customers. (Hint: The phrase "station A is capturing 7% of station B's customers" means that 7% of the listeners are moving from B to A, not the other way around.) At the same time, station A is losing only 2% of its customers to B and 2% of its customers to C. Additionally, each month 1% of B's customers switch to C, and 1% of C's customers switch to B. Initially, A and B each have 30% of the listeners and C has 40%. Use this information to answer the following questions. (Give your answers correct to three decimal places. Note that you are asked to give decimal values and not percentages. For example, you would need to enter 0.628 as opposed to 62.800%.) (a) What fraction of the listeners will A have after 3 months? (b) What fraction of the listeners will B have after…arrow_forward
- A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 25% of the rooms at the Ramada Inn, in 35% of the rooms at the Sheraton, and in 40% of the rooms at the Lakeview Motor lodge, what is the probability that (a) a client will be assigned a room with faulty plumbing? (b) a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? (c) a person with a room having no faulty plumbing was assigned accommodations at the Lakeview Motor Lodge?arrow_forwardA large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 25% of the rooms at the Ramada Inn, in 35% of the rooms at the Sheraton, and in 40% of the rooms at the Lakeview Motor lodge, what is the probability that (a) a client will be assigned a room with faulty plumbing? (b) a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? (c) a person with a room having no faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? Round off the final answer to five decimal places.arrow_forwardA large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the lakeview Motor Lodge. If the plumbing is faulty in 5% of the rooms at the Ramadan Inn, in 4% of the rooms at the Sheraton, and in 8% of the rooms at the Lakeview Motor Lodge, what is the probability that (a) a client will be assigned a room with faulty plumbing? (b) a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge?arrow_forward
- Jenn works for a company that helps customers with various computer problems and she is in charge of computers that quit working either because they have virus A or computer virus B. Jenn estimates that about 20% of customers come in because of virus A and the remaining come in because of virus B . If the computer is infected by virus A, Jenn has a 35% chance of fixing the problem. But if the computer has virus B, she has a 95% chance of fixing the problem. 1. A random computer is selected from the shop. What is the probability that it can't be fixed by Jenn? Show your work on paper 2. A random computer is selected and it is one Jenn can't fix. What is the probability that it was infected with virus A? Show your work on paperarrow_forwardIn the 2020 election, exit polls showed that 37% of voters identified as Democrat, 36% as republican, and the rest as independent. Of Democrats, 94% voted for President Biden, while 5% voted for former President Trump. Of Republicans, 6% voted Biden, while 94% voted Trump. And independents voted 54% for Biden and 41% for Trump. Note that some of these do not add up to 100% as some people may have voted third party, also we are rounding to the nearest integer percentage. What percentage of the total voters voted for Trump?arrow_forwardA large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 5% of the rooms at the Ramada Inn, in 4% of the rooms at the Sheraton, and in 8% of the rooms at the Lakeview Motor Lodge, what is the probability that a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge? Select one: O a. 0.666 O b. 0.219 O c. 0.444 O d. 0.719arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill