A new subscription based software company is set to release later this month. You must figure out the financial workings before it is released to the public in order for it to be successful. Based on the function R(x) = 375x0.25x² + 1000 √√x solve the tasks given with detailed work and explanations given. 1. The company has a target capacity to handle up to 2500 subscribers per month. Determine the number of subscribers the company should aim for to maximize the monthly revenue. What is the maximum revenue in dollars? 2. Find the number of subscribers (in thousands) the company should aim for to achieve the highest revenue, up to their capacity of 3000 subscribers per month. Then, determine whether this revenue point is an absolute maximum or a local maximum, using calculus terminology. 3. Find the number of subscribers (in thousands) that the company must acquire in order to achieve a marginal revenue of $250 per subscriber. If the revenue function never achieves this marginal revenue, explain why not. 4. If the company was considering to implement a marketing campaign to increase its subscriber base. The marketing campaign is estimated to increase the number of subscribers by 10% per month. If the company decides to start the marketing campaign, how many months will it take for the revenue to surpass $1,000,000?
A new subscription based software company is set to release later this month. You must figure out the financial workings before it is released to the public in order for it to be successful. Based on the function R(x) = 375x0.25x² + 1000 √√x solve the tasks given with detailed work and explanations given. 1. The company has a target capacity to handle up to 2500 subscribers per month. Determine the number of subscribers the company should aim for to maximize the monthly revenue. What is the maximum revenue in dollars? 2. Find the number of subscribers (in thousands) the company should aim for to achieve the highest revenue, up to their capacity of 3000 subscribers per month. Then, determine whether this revenue point is an absolute maximum or a local maximum, using calculus terminology. 3. Find the number of subscribers (in thousands) that the company must acquire in order to achieve a marginal revenue of $250 per subscriber. If the revenue function never achieves this marginal revenue, explain why not. 4. If the company was considering to implement a marketing campaign to increase its subscriber base. The marketing campaign is estimated to increase the number of subscribers by 10% per month. If the company decides to start the marketing campaign, how many months will it take for the revenue to surpass $1,000,000?
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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Based on this question add on the following list and rewrite the question.
1. Is 'x' defined in thousands or is it just 1 subsriber = 1 x ?
2. Is the y value for R(x) in dollars or thousands?
3. Are negative numbers for the range allowed?
4. In part 4 should a new equation be made for 'x' [example: x=(1+0.1)^m] and then be substituted into the revenue equation?
Transcribed Image Text:A new subscription based software company is set to release later this month. You
must figure out the financial workings before it is released to the public in order
for it to be successful. Based on the function
R(x) = 375x0.25x² + 1000 √√x solve the tasks given
with detailed work and explanations given.
1. The company has a target capacity to handle up to 2500 subscribers per
month. Determine the number of subscribers the company should aim for
to maximize the monthly revenue. What is the maximum revenue in
dollars?
2. Find the number of subscribers (in thousands) the company should aim for
to achieve the highest revenue, up to their capacity of 3000 subscribers per
month. Then, determine whether this revenue point is an absolute
maximum or a local maximum, using calculus terminology.
3. Find the number of subscribers (in thousands) that the company must
acquire in order to achieve a marginal revenue of $250 per subscriber. If
the revenue function never achieves this marginal revenue, explain why
not.
4. If the company was considering to implement a marketing campaign to
increase its subscriber base. The marketing campaign is estimated to
increase the number of subscribers by 10% per month. If the company
decides to start the marketing campaign, how many months will it take for
the revenue to surpass $1,000,000?
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