MARKET SHARE At a certain university, three bookstores- the University Bookstore, the Campus Bookstore, and the Book Mart currently serve the university community. From a survey conducted at the beginning of the fall quar- ter, it was found that the University Bookstore and the Campus Bookstore each had 40% of the market, whereas the Book Mart had 20% of the market. Each quarter, the University Bookstore retains 80% of its customers but loses 10% to the Campus Bookstore and 10% to the Book Mart. The Campus Bookstore retains 75% of its customers but loses 10% to the University Bookstore and 15% to the Book Mart. The Book Mart retains 90% of its customers but loses 5% to the University Bookstore and 5% to the Campus Bookstore. If these trends continue, what percent- age of the market will each store have at the beginnin the second quarter? The third quarter?

MARKET SHARE At a certain university, three bookstores- the University Bookstore, the Campus Bookstore, and the Book Mart currently serve the university community. From a survey conducted at the beginning of the fall quar- ter, it was found that the University Bookstore and the Campus Bookstore each had 40% of the market, whereas the Book Mart had 20% of the market. Each quarter, the University Bookstore retains 80% of its customers but loses 10% to the Campus Bookstore and 10% to the Book Mart. The Campus Bookstore retains 75% of its customers but loses 10% to the University Bookstore and 15% to the Book Mart. The Book Mart retains 90% of its customers but loses 5% to the University Bookstore and 5% to the Campus Bookstore. If these trends continue, what percent- age of the market will each store have at the beginnin the second quarter? The third quarter?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.;50% of the time she travels on airline #1, 30% of the time on airline #2, and the remaining 20% of the time on airline #3. For airline #1, flights are late into D.C.30% of the time and late into L.A.10% of the time. For airline #2,these percentages are 25% and 20%,whereas for airline #3 the percentages are 40% and 25%.If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1,#2, and #3? Assume that the chance of a late arrival in L.A.is unaffected by what happens on the flight to D.C. [ Hint: From the tip of each first generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late,1late, and 2 late.]
Jose visits campus every Thursday evening. However, some days the parking garage is full, often due to college events. There are academic events on 35% of evenings, sporting events on 20% of evenings, and no events on 45% of evenings. When there is an academic event, the garage fills up about 25% of the time, and it fills up 70% of evenings with sporting events. On evenings when there are no events, it only fills up about 5% of the time. If Jose comes to campus and finds the garage full, what is the probability that there is a sporting event? A. Draw a tree diagram (marginal probabilities in the primary branch and conditional probabilities in the secondary branches). B. What is the probability that there is a sporting event when Jose finds the garage full?
Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus (New York Daily News). The 2017 market shares are Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models comprising the remaining 23%. A sample of 400 compact car sales in Chicago showed the following number of vehicles sold. Excel File: data12-27.xlsx Honda Civic 98 Toyota Corolla 72 Nissan Sentra 54 Hyundai Elantra 44 Chevrolet Cruze 42 Ford Focus 25 Others 65 Use a goodness of fit test to determine whether the sample data indicate that the market shares for cars in Chicago are different than the market shares suggested by nationwide 2017 sales. Using a 0.05 level of significance, what is the p-value? Use Table 3 of Appendix B. The p-value is - Select your answer - What is your conclusion? Conclude that the markets shares for the seven compact…
. In 2010, of a total of 67,000 rooms on the Las Vegas Strip, Caesars Entertainment managed 22,880, while MGM Resorts managed over 12,000. However, owing to the Great Recession and new hotel openings, between 2008 and 2010, MGM's hotel occupancy decreased from 92% to 89%, while its average daily room rate fell from $148 to $108. Meanwhile, CityCenter, managed by MGM Resorts, and the Cosmopolitan opened with 4,000 and 3,000 rooms respectively, and the 1,720-room Sahara closed. (Sources: Caesars Entertainment Corp., Annual Report 2010; MGM Resorts, Annual Report 2010; "Sahara's closure on May 16 will mark `the end of an era'," Las Vegas Sun, March 11, 2011.) (a) Using a suitable figure, explain how the opening of CityCenter and the Cosmopolitan affects the residual demand for an existing hotel and how it should adjust prices. (b) If MGM Resorts had not reduced its room rates, what would have been the effect on occupancy? (c) Use the Cournot model to explain…
A software company keeps their important files on a CD, on a flash drive and on a Googledrive as a backup copy. Suppose it is known that they keep their 15% files on a CD, 35%files on a flash drive and 50% files on a Google drive. From the past experience, it is knownthat 50%, 30% and 5% files are corrupted when it was backed-up onto the CD, onto theflash drive, and onto the Google drive, respectively. If a randomly chosen file was foundto be corrupted, what is the probability that the file was not kept on Google drive or kepton CD?
WXXX, WYYY, AND WZZZ are three radio stations that compete for listeners. Each month some of the listeners switch from one station to another while some remain loyal to their current station. It has been found that each month: 20% of the listeners of WXXX switch to WYYY 10% of the listeners of WXXX switch to WZZZ 30% of the listeners of WYYY switch to WXXX 10% of the listeners of WYYY switch to WZZZ 20% of the listeners of WZZZ switch to WXXX 30% of the listeners of WZZZ switch to WYYY Currently, the listening audience is divided as follows: 25% listen to WXXX 40% listen to WYYY 35% listen to WZZZ 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 WZZZ have after 2 months? (b) What fraction of the listeners will WXXX have after 3 months? (c) What fraction of…
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? Round off the final answer to five decimal places.
A 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. 0.719
A stable population of 35,000 birds lives on three islands. Each year 10% of the population on island A migrates to island B, 20% of the population on island B migrates to island C, and 5% of the population on island C migrates to island A. Find the number of birds on each island if the population count on each island does not vary from year to year.
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Florrie’s Fashion Store and Mary’s market stall both sell a particular style of sweatshirt. They arethe only outlets for the garment in the area, with Florrie’s accounting for 70% of the total numbersold and Mary’s accounting for the remainder. Unfortunately colour dye that faded prematurely wasused to manufacture the first batches of the product. The supplier estimates that 15% of the stocksupplied to Florrie and 25% of the stock supplied to Mary have this problem. Use Bayes’ rule to findthe probability that if a sweatshirt is defective it was sold by Mary.