So Lost!

[gilliesam]

I need help with the following problem:
Your company would like to know how sales levels affect profits. If too few items are sold, then there is a loss. Even if too many items are sold, however, the company can lose money (likely because of low pricing). It is good to know how many items can be sold for there to be profit.
Functions are very useful in many areas, such as in business to find the profit an organization is making. For example, the following function expresses profit in terms of the number of phones sold by a particular company:

P(x) = –x² + 110x – 1,000​

This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smartphones.

1. Compute the following: P(5), P(50), and P(120). Then, interpret the results.
2. Graph the function using the desired graphing program. Paste the graph that you create into your assignment.
3. Discuss and interpret the meaning where the profit function crosses the x-axis. Refer to last week’s assignment concerning break-even points, and interpret the graph. Also, discuss where the graph is above and below the x-axis, explaining what that means in terms of profitability.

For part a. I got P(5)=-425, P(50)=7,000 and P(120)=26,600 and I don't know if that's right. Additionally, I'm using www.padowan.dk/graph to graph this and I don't know how to graph this correctly. All I get are three straight lines running parallel to the x-axis. My professor is so unclear and I'm completely confused. Any help would be very much appreciated!

 

[mmm4444bot]

P(x) = –x² + 110x – 1,000

For part [1] I got P(5)=-425, P(50)=7,000 and P(120)=26,600

None of these results are correct. I'll do an example, using 25,000 sales.

EG: Find P(25)

P(25) = -(25^2) + 110(25) - 1000

25 squared is 625

110(25) is 2750
​

P(25) = -625 + 2750 - 1000

P(25) = 1125

This shows that 25,000 smartphone sales yield a profit of $1,125,000.

If you cannot find the errors in your calculations, please show your work.

 

[mmm4444bot]

When typing the polynomial in your grapher, use the caret symbol ^ for exponentiation. (It is shift-6, on most keyboards.)

Use an asterisk * for a multiplication sign.

Do not type any commas in numbers.

In other words, your typing should look like this:

-x^2 + 110*x - 1000

---

On the menu bar, click "Function"

From the drop-down menu, select "Insert function…"

This brings up the "Insert Function" dialog box. Fill in the top part, as shown below, and then click the [OK] button.



At this point, you will probably not see the graph because it lies outside the default viewing window.

To automatically change the axes to fit the graph, click "Zoom" on the menu bar and select "Fit". Then click "Zoom" again and select "Fit" a second time.

 

[gilliesam]

Thank you!

I realized I wasn't making the first number negative, which really messed things up.

I got P(5)=475, P(50)=2000 and P(120)=-2200 ... all of which made a lot more sense in the context of the word problem. And the graph came out perfectly.

Thank you so much for your help!

 

[gilliesam]

P(5)=-475 ... can't forget that part!