Marginal Analysis, i need help answering this question
Interns, Mr. Howell, the prestigious founder and owner of our company would like you to perform an analysis on the company's weekly revenues. He is requiring that the current weekly marginal revenue be at least $5,000 per week and if it is not currently at that level how fast should sales be changing to reach the target marginal revenue level. The most current information regarding weekly revenues can be found in Mr. Howell's email below. "Mr. Kleppin. It has come to my attention that our weekly marginal revenues may not be at the minimum level of $5,000 per week as I required. According to the sales report, we are currently selling 1,000 DVD's per week and sales are currently rising by 200 DVD's a week (gotta love the Marvel Universe! Customers can't get enough!). They also inform me that our current selling price is $20 and that the price is dropping by $1 per week to encourage more sales. I would like you, Mr. Kleppin, to give the interns a chance to earn one of the 10 available positions at the end of their internship by giving them the opportunity to do the analysis. Again, I need to know if we are at the minimum level of $5,000 per week in marginal revenue, and if not, at what level should our sales per week be at so as to achieve the minimum marginal revenue level." You will have just over one week to submit your analysis for consideration. Mr. Howell requires the information for the next administrative meeting, so you will need to submit your analysis by 11:59pm on Monday, June 15. In case you didn't know, Mr. Howell is a stickler for precision and accuracy so I have provided a rubric by which your analysis will be evaluated. You need to be using the derivative rules from chapter 11 (especially implicit differentiation) for the analysis. You need to interpret the English descriptions into their mathematical symbols. For example, if i am selling a product and in order to increase my sales per month, I decrease the price per month by a certain amount. Both my monthly sales (quantity and monthly price are both with respect to TIME months). Soita quantity sold each month and the price the unit is sold for each month, then da/dt represents the CHANGE IN QUANTITY WITH RESPECT TO THE CHANGE IN TIME. And dpt represents the CHANGE IN PRICE WITH RESPECT TO THE CHANGE IN TIME. So if the price is dropping by $5 each month, then dpt - 5. With this price decrease the quantity sold each month is increasing by 30 units per month, sodat 30. You are also writing this to your boss, so be professional! Interns, Mr. Howell, the prestigious founder and owner of our company would like you to perform an analysis on the company's weekly revenues. He is requiring that the current weekly marginal revenue be at least $5,000 per week and if it is not currently at that level how fast should sales be changing to reach the target marginal revenue level. The most current information regarding weekly revenues can be found in Mr. Howell's email below. "Mr. Kleppin. It has come to my attention that our weekly marginal revenues may not be at the minimum level of $5,000 per week as I required. According to the sales report, we are currently selling 1,000 DVD's per week and sales are currently rising by 200 DVD's a week (gotta love the Marvel Universe! Customers can't get enough!). They also inform me that our current selling price is $20 and that the price is dropping by $1 per week to encourage more sales. I would like you, Mr. Kleppin, to give the interns a chance to earn one of the 10 available positions at the end of their internship by giving them the opportunity to do the analysis. Again, I need to know if we are at the minimum level of $5,000 per week in marginal revenue, and if not, at what level should our sales per week be at so as to achieve the minimum marginal revenue level." You will have just over one week to submit your analysis for consideration. Mr. Howell requires the information for the next administrative meeting, so you will need to submit your analysis by 11:59pm on Monday, June 15. In case you didn't know, Mr. Howell is a stickler for precision and accuracy so I have provided a rubric by which your analysis will be evaluated. You need to be using the derivative rules from chapter 11 (especially implicit differentiation) for the analysis. You need to interpret the English descriptions into their mathematical symbols. For example, if i am selling a product and in order to increase my sales per month, I decrease the price per month by a certain amount. Both my monthly sales (quantity and monthly price are both with respect to TIME months). Soita quantity sold each month and the price the unit is sold for each month, then da/dt represents the CHANGE IN QUANTITY WITH RESPECT TO THE CHANGE IN TIME. And dpt represents the CHANGE IN PRICE WITH RESPECT TO THE CHANGE IN TIME. So if the price is dropping by $5 each month, then dpt - 5. With this price decrease the quantity sold each month is increasing by 30 units per month, sodat 30. You are also writing this to your boss, so be professional
