Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was 550 log-ons permonth. When you lowered the price to $2.50, the demand increased to 825 log-ons per month.(a) Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x.R(x) =(b) Your Internet provider charges you a monthly fee of $50 to maintain your site. Express your monthly profit P as a function of the log-on fee x.P(x) =Determine the log-on fee you should charge to obtain the largest possible monthly profit (in dollars).$What is the largest possible monthly profit (in dollars)?$

explained below Explanation:Step 1:(a) Construct a linear demand function for your website and hence…

Answered: Website Profit You operate a gaming…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Membership at a private arcade club costs a one-time initiation fee of $50 plus $10 per month. Part A: Write a function expressing the total amount of money spent on membership as a function of the number of months. Part B: Identify the independent variable and the dependent variable in this situation. Part C: How much total money has been spent on membership after 12 months?
Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was 1120 log-ons per month. When you lowered the price to $2.50, the demand increased to 1400 log-ons per month. (a) Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x. R(x) -560x²+2800x = (b) Your Internet provider charges you a monthly fee of $50 to maintain your site. Express your monthly profit P as a function of the log-on fee x. P(x): -1120x + 2800 Determine the log-on fee you should charge to obtain the largest possible monthly profit (in dollars). X = $ 2.5 X What is the largest possible monthly profit (in dollars)? $ 5550 X
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =
A dairy spends $24,000 per year to maintain its barns and equipment. It costs $2000 per year to feed and care for each dairy cow. (a) Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. E = (b) Use functional notation to express the total expense if the dairy has 40 cows. E(40) E(40C) 40E E(2000) E(24,000) (c) Calculate the value from part (b). $
In 2011 online sales were $192 billion, and in 2015 they were $264 billion. (a) Find a linear function S that models these data, where S is the sales in billions of dollars and x is the year. Write S(x) in slope-intercept form. (b) Interpret the slope of the graph of S. (c) Determine when online sales were $246 billion. ..... (a) Write S(x) in slope-intercept form. S(x) = %3D (b) Interpret the slope of the graph of S. Choose the correct answer below. O A. Sales decreased by $18 billion in next 4 years. B. Sales decreased, on average, by $18 billion/yr. C. Sales increased, on average, by $18 billion/yr. D. Sales increased by $18 billion in next 4 years. (c) Online sales were $246 billion in the year

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