Suzy, an analyst at a local toy company, receives the following email from her marketing department: "According to our data, the demand for Slinkies can be modeled by p=q50, where p is the price per Slinky (in dollars) and q is the quantity. Manufacturing has estimated that the cost (in dollars) of producing q Slinkies is given by C=0.5q+500. We are reaching out to you to help us establish the number of Slinkies we must sell in order for the company to make the most money. Thank you in advance. We look forward to hearing back from you." Analysis 1. Identify the needs of the company, and list the information given in the email that Suzy will use to address their needs. (Use complete sentences without any calculations.) Inquiry 2. What missing information must Suzy determine in order to solve the company's request? (Use complete sentences without any calculations.) 3. Use the information given to create the profit function P(q). Show your work clearly and simplify your answer. 4. Use calculus to calculate the quantity q that will maximize the profit function P(q). Make sure you verify that your answer yields the maximum profit. Show your work clearly and indicate which test you are using. Synthesis 5. Write an email response from Suzy to the marketing department clearly detailing her findings. Remember that the marketing department is not necessarily familiar with calculus, so take your audience into consideration. (Use complete sentences.)