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Project II- Point of Diminishing Returns Name: ____________________________
Due: Monday, June 24, 2013
Please read each question carefully and be sure to answer all parts. Show all of your work.
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The total amount of revenue made by the Miramar Resort Hotel is given by the function
, , where x is the amount of money the hotel spends on advertising its services, and where both revenue and x are measured in thousands.
1. Using Wolfram Alpha, graph the revenue function over the given domain and paste the graph here.
2. Compute the marginal revenue function and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing and where revenue is decreasing. Write your answers using interval notation.
(0, 150) Revenue is increasing (150,300) Revenue is decreasing.
3. How much money (in dollars) should the hotel spend on advertising to maximize its revenue? What is the maximum revenue in dollars?
The hotel should spend $250,000 to reach their maximum revenue.
4. Compute the second derivative of R(x). Copy and paste the graph of the second derivative here. On which intervals is the function concave up? Explain what is happening to revenue on this interval.
According to the graph the function is not a concave up but is concave down at all points. After 150 the revenue is turning into a loss. This means that spending more will lead to losses.
5. On which intervals is the function concave down? Explain what is happening to revenue on these intervals.
The function is concave down at interval (0,150). The revenue is constantly decreasing at this interval.
6. What is the point of diminishing returns? Explain the significance of this point with respect to marginal revenue. What is the production level and the revenue at this point?
The point of diminishing return is the point
Due: Monday, June 24, 2013
Please read each question carefully and be sure to answer all parts. Show all of your work.
____________________________________________________________________________
The total amount of revenue made by the Miramar Resort Hotel is given by the function
, , where x is the amount of money the hotel spends on advertising its services, and where both revenue and x are measured in thousands.
1. Using Wolfram Alpha, graph the revenue function over the given domain and paste the graph here.
2. Compute the marginal revenue function and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing and where revenue is decreasing. Write your answers using interval notation.
(0, 150) Revenue is increasing (150,300) Revenue is decreasing.
3. How much money (in dollars) should the hotel spend on advertising to maximize its revenue? What is the maximum revenue in dollars?
The hotel should spend $250,000 to reach their maximum revenue.
4. Compute the second derivative of R(x). Copy and paste the graph of the second derivative here. On which intervals is the function concave up? Explain what is happening to revenue on this interval.
According to the graph the function is not a concave up but is concave down at all points. After 150 the revenue is turning into a loss. This means that spending more will lead to losses.
5. On which intervals is the function concave down? Explain what is happening to revenue on these intervals.
The function is concave down at interval (0,150). The revenue is constantly decreasing at this interval.
6. What is the point of diminishing returns? Explain the significance of this point with respect to marginal revenue. What is the production level and the revenue at this point?
The point of diminishing return is the point