Table for determining the value of B to use: Setting: You are making prime magic wands using phoenix feathers. The price and Cost are given at the bottom of the page. You will need to use what we have been studying about quadratic functions to complete this project. See the coversheet for general directions. 1. Find R(x) 2. Find the x intercepts, y intercept and vertex for R(x). Show all computations. Values must be exact. 3. Graph R(x). To graph R(x) use the information found above and plot at least 2 additional points to get a good graph. Provide a table with the graph giving the points found in part 2 as well as the additional 2 points. Put this table on the same sheet as the graph. Remember the graph must be hand drawn on a full sheet of paper. 4. Discuss what the graph of R(x) reveals about the revenue for this company. What is an appropriate domain for the revenue function? Think about this, what values yield realistic values for the revenue. This function represents the money coming into the company. So including negative x values or values that yield a negative revenue would not be appropriate. This answer is to
be an interval, not a single value. Discuss why this the appropriate domain. 5. Find the profit function, P(x), for this company. (The work to find this function must be provided in the appropriate place.) 6. Find the x intercepts, y intercept and vertex for P(x). Work must be given. Values must be exact. 7. Graph P(x). To graph P(x) use the information found above and plot at least 2 additional points to get a good graph. Provide a table with the graph giving the points found in part 6 as well as the additional 2 points. 8. Discuss what the graph of P(x) reveals about the profit for this company. Does it give an indication as to a cap for how large the production should be? (IE, is there a value where if more is made the company loses money?) Why is that the value you selected for the maximum production level? Is there a minimum level of production that the company should have? Why? What is the break even quantity? What does this break even quantity indicate about the desired production levels for this company? 9. If the current production level is 350 wands a week, should you increase the production by 10%? Why or why not?