Price war a small town on a major highway has only two gas stations: station
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- Satellite Television: Two competing companies offer satellite television to a city with 100,000 households. Gold Satellite System has 25,000 subscribers and Galaxy Satellite Network has 30,000 subscribers. (The other 45,000 households do not subscribe.) The matrix shows the percent changes in satellite subscriptions each year. FromGoldFromGalaxyFromNon-subscriberPercentChangesPercentChanges{ ToGoldToGalaxyToNonsubscriber [ 0.700.150.150.200.800.150.100.050.70 ] (a) Find the number of subscribers each company will have in 1 year using matrix multiplication. Explain how you obtained your answer. (b) Find the number of subscribers each company will have in 2 years using matrix multiplication. Explain how you obtained your answer. (c) Find the number of subscribers each company will have in 3 years using matrix multiplication. Explain how you obtained your answer. (d) What is happening to the number of subscribers to each company? What is happening to the number of nonsubscribers?arrow_forwardThe Camera Shop sells two popular models of digital SLR cameras (Camera A Price: $200, Camera B Price: $300). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model: NA = 198 - 0.5PA + 0.25PB NB = 305 + 0.07PA - 0.6PB Construct a model for the total revenue and implement it on a spreadsheet. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10. Max revenue occurs at Camera A price of $ Max revenue occurs at Camera B price of $arrow_forwardOn-Time Performance of Airlines. The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Airport. Suppose that the percentage of on-time flights reported was 76.8% for JetBlue, 71.5% for United, and 82.2% for US Airways. Assume that 30% of the flights arriving at terminal C are JetBlue flights, 32% are United flights, and 38% are US Airways flights. Develop a joint probability table with three rows (the airlines) and two columns (on-time and late). Answer Let Given: Joint probabilities using the multiplication law With the marginal probabilities , , and given, the joint probability table can then be shown as follows. An announcement is made that Flight 1382 will be arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time? Answer Using the joint probability table, the probability of an on-time flight is the marginal…arrow_forward
- Depression and insomnia often go hand-in-hand, and sometimes it is unclear which of the two should be the primary subject of treatment in individuals suffering from insomnia. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of both antidepressants and sleeping pills. Mendoza's current business model describes the following breakdown of America's approximately 50 million adults suffering from insomnia: 17% use both antidepressants and sleeping pills regularly, 24% use only antidepressants regularly, 15% use only sleeping pills regularly, and the remaining 44% use neither antidepressants nor sleeping pills regularly. A recent issue of the psychiatry journal Patterns contains a study on insomnia. In the study, 200 American adults suffering from insomnia (but otherwise chosen at random) were asked about their use of antidepressants and sleeping pills. The breakdown of their answers is given by the top row…arrow_forwardA mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows. Money-market Intermediate bond Short bond Need Help? Long bond Submit Answer 25% 14% 5% Read It 5% High-risk stock Moderate-risk stock Balanced A customer who owns shares in just one fund is randomly selected. (a) What is the probability that the selected individual owns shares in the balanced fund? Watch It (b) What is the probability that the individual owns shares in a bond fund? 19% (c) What is the probability that the selected individual does not own shares in a stock fund? 25% 7% Master Itarrow_forwardA new website allows consumers to purchase various automobiles via the internet and then take delivery at a local dealer. The following table shows the retail price of the cars on the website. Brand A Brand B 17,000 11, 000 23, 000 27, 000 52, 000 Compact 19, 000 34, 000 50, 000 Midsize Luxury Pickup The dealers makes the following profit: On compact cars they make 12% On midsize cars they make 13%, On luxury cars they make 10% On pickup trucks they make 19 % In your notebook, create a matrix with all of the vehicle prices in it. Then demonstrate how matrix multiplication with the following profit percentage matrix (shown below) can be used to find the profit per vehicle. Find a matrix of profit per car. THE 0.12 0 0.13 0 0. 0. 0.1 0 0.19 The profit matrix is Reading from the profix matrix, how much profit does the dealer make if they sell 5 Brand B luxury cars?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,