Assume pollutex inc. produces paper in its plant located on lake ontario, half a mile away from cleanair camping. pollutex employs an obsolete production process, dumping pollutants in the lake. the camp has experienced a steady decline in the number of attendees since pollutex moved nearby. in particular, the owners forecast that cleanair camping will generate a profit of only $50,000 a year in the future, which is $150,000 less than the one generated before pollutex moved nearby. a cleaner production process is available, which would not require dumping the pollutants in the lake. however, converting the plant would increase yearly costs by $100,000. is the current situation pareto efficient?

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

The state troopers in one state have a motto, “nine you’re fine; ten you’re mine,” which is the standard that they use for pulling over speeders on the state highways. in other words, if the posted speed limit is 55 mph, drivers can drive at a rate up to 64 mph without fear of getting a ticket. which of the following best describes the ethical culture in the state? a. the troopers are following a standard of positive law. b. the troopers are following a normative standard. c. the troopers are following a headline test. d. the troopers are following the blanchard/peale standard.