General Directions:

• The coversheet is to be stapled to all of your work. Work will not be accepted if it is not stapled.
• The work for this project is to be well organized.
• Graphs should be on graph paper and identified as to what the graph is. Graphs are to be hand drawn, no computer generated graphs.
• Use a full sheet of graph paper for each graph. Select a scale and place the x and y axes in such a way that the graph is using most of the sheet of paper. When referring to a graph in the written portion of this project, it should be referenced by its name.
• The scale on the horizontal and vertical axes for the graphs must be consistent. Values on the both scales must be labeled periodically.
• The written summaries for this project should be typed. Computations can be hand written, but they should be in the appropriate places. This will require leaving space in the Word document to write the computations in. All written summaries should use complete sentences and correct grammar. Written computations MUST be inserted within the document at the appropriate places.
• It is important that all work is in the order stated. The only thing that can be out of order are the actual graphs.

Table for determining the value of B to use:

 A 11 12 13 14 15 16 17 18 19 B 1879 2104 1348 1499 2316 2187 1894 1289 1579 A 20 21 22 23 24 25 26 27 28 B 1875 1583 1197 1157 1627 2179 1487 1955 1535 A 29 30 31 32 33 34 35 36 37 B 1554 1359 1612 1085 1158 1287 1487 1287 2454

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?

• 6 years ago
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