rite-cut riding lawnmowers obey the demand equation p equals negative startfraction 1 over 20 endfraction x plus 990 . the cost of producing x lawnmowers is given by the function upper c (x )equals 110 x plus 4000.
a) express the revenue upper r as a function of x.
b) express the profit upper p as a function of x.
c) find the value of x that maximizes profit. what is the maximum profit?

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?

Suppose an economy has only two sectors: goods and services. each year, goods sells 80% of its outputs to services and keeps the rest, while services sells 62% of its output to goods and retains the rest. find equilibrium prices for the annual outputs of the goods and services sectors that make each sector's income match its expenditures.

Your sister is thinking about starting a new business. the company would require $375,000 of assets, and it would be financed entirely with common stock. she will go forward only if she thinks the firm can provide a 13.5% return on the invested capital, which means that the firm must have an roe of 13.5%. how much net income must be expected to warrant starting the business? a. $41,234b. $43,405c. $45,689d. $48,094e. $50,625