MYou will use P(x)= −0.2×2 + bx – c where (−0.2×2 + bx) represents the business’ variable profitand c is the business’s fixed costs.So, P(x) is thestore’s total annual profit (in $1,000) based on the number of items sold, x.1. Choose a valuebetween 100 and 200 for b. That value does not have to be a whole number.2. Think aboutand list what the fixed costs might represent for your fictitious business (becreative). Start by choosing a fixed cost, c, between $5,000 and $10,000,according to the first letter of your last name from the values listed in thefollowing chart:If your last namebegins with the letterChoose a fixedcost betweenA–E$5,000–$5,700F–I$5,800–$6,400J–L$6,500–$7,100M–O$7,200–$7,800P–R$7,800–$8,500S–T$8,600–$9,200U–Z$9,300–$10,000Page 2 of 43. Important: ByWednesday night at midnight, submit a Word document with only your name andyour chosen values for b and c above in Parts 1 and 2. Submit this in the Unit2 IP submissions area. This submitted Word document will be used to determinethe Last Day of Attendance for government reporting purposes.4. Replace b andc with your chosen values in Parts 1 and 2 in P(x) = −0.2×2 + bx − c. This isyour quadratic profit model function. State that quadratic profit modelfunctions equation.5. Next, choose 5values of x (number of items sold) between 500 and 1,000. Think about thegeneral characteristics of quadratic function graphs (parabolas) to help youwith choosing these 5 values of x.6. Plug these 5values into your model for P(x), and evaluate the annual business profit giventhose sales volumes. (Be sure to show all of your work for these calculations.)7. Use the 5ordered pairs of numbers from 5 and 6 and Excel or another graphing utility tograph your quadratic profit model, and insert the graph into your Word answerdocument. The graph of the quadratic function is called a parabola.8. What is the vertexof the quadratic function graph? (Show your work details, or explain how youfound the vertex.)9. What is theequation of the line of symmetry? Explain how you found this equation.10. Write thevertex form for your quadratic profit function.11. Is there amaximum profit for your business? If so, how many items must be sold to producethe maximum profit, and what is that maximum profit? If your quadratic profitfunction has a maximum, show your work or explain how the maximum profit figurewas obtained.12. How wouldknowing the number of items sold that produces the maximum profit help you torun your business more effectively.13. Analyze theresults of these profit calculations and give some specific examples of howthese calculations could influence your business decisions.14. Which of theintellipath Learning Nodes seemed to be most helpful in completing thisassignment?
