To generate a profit from its o'Books e-book service, OHaganBooks.com needs to know how the demand for novels depends on the price it charges.During the first month of the service, it was charging $10 per novel and sold 350. Lowering the price (p) to $5.50 per novel had the effect of increasingdemand (q) to 620 novels per month.(a) Use the given data to construct a linear demand equation q(p) per month.q(p) =(b) Use the demand equation you constructed in part (a) to estimate the demand per month if the price were raised to $15 per novel.novels per month(c) Author royalties and copyright fees cost the company an average of $3 per novel, and the monthly cost of operating and maintaining the serviceamounts to $900 per month. Using this information, determine which of the three prices ($5.50, $10, and $15) would result in the largest profit,and the size of that profit.profit maximizing price $maximum profit$

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company manufactures and sells water bottles. Last year the company sold the water bottles for $14 each and the sales averaged 90 bottles per day. When the company increased the price by $4, the average decreased by 5 sales per day. (a) Find the demand function (price p as a function of units sold x), assuming that it is linear. (b) If the material for each water bottle costs $6, what should the selling price be to maximize the profit?
A mobile phone provider charges $3.75 plus $0.15 per minute for overseas calls. (i) Write a linear model which shows the cost C, in dollars, for a client talking x minutes. (ii) How much would it cost the client for an overseas call with a duration of 55 minutes?
Television Advertising As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 21 contracts. This is down 6 contracts from the figure last year, when your company charged only $2,300. (a) Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo charges for development. q(p) = (b) On average, Montevideo bills for 40 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. R(p) = (c) The costs to Montevideo Productions are estimated as follows. Fixed costs: $140,000 per month Variable costs: $60,000 per contract Express Montevideo Productions' monthly cost as a function of the number q of contracts. C(q) = =…
Refer to the picture below.
Television Advertising As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 21 contracts. This is down 6 contracts from the figure last year, when your company charged only $2,300. (a) Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo charges for development. q(p) = -0.01p+ 50 (b) On average, Montevideo bills for 40 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. R(p): -0.4p² + 2000p (c) The costs to Montevideo Productions are estimated as follows. Fixed costs: $140,000 per month Variable costs: $60,000 per contract Express Montevideo Productions' monthly cost as a function of the number q…
A department store manager has determined that when the price of a skirt was $12 she sold 100 skirts per month. However, only 80 skirts were sold per month when the price was raised to $14. Assuming a linear demand functions, determine the price that would maximize the revenue.
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the function y = 0.0682x² + 1.76x + 96.0 where x is the number of years past 2010 and y is the CPI in dollars. With a reference of 100 in 2012, a CPI of 120 in another year means that goods and services costing $100 in 2012 are expected to cost $120 in that other year (a) Use a table to determine a viewing window that shows a complete graph of this function for the years from 2010 to 2050. 2050 corresponds to an x value of which corresponds to a y value of The y maximum should be -Select-than this function value (b) Graph the function. y 300 250 200 150 100 50 0 y 300 250 200 150 100 50 X = Need Help? 51 F Partly sunny 10 10 20 Read It 20 30 30 T X 40 40 y 300 250 200 150 100 50 0 0 10 (c) Use the graph to estimate when the CPI is predicted to reach 250. (Round your answer to the nearest whole year.) years 20 30 Q Search 40 y 300 250 200…
A tour guide charges a price of $600 per person for a jungle tour and typically 8 persons sign up for the tour. One time the guide offers the jungle tour at a discounted price of $525 per person and finds that 11 persons sign up for the tour. Assuming the demand trend is linear and that for each price drop of $25, one more person is interested in the tour, what size of group a will produce the largest revenue for the tour guide? I
Needed to be solved last part correctly in 30 minutes and get the thumbs up please show neat and clean work
Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence.

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