5.5+Revisiting+Jean’s+Problem

// Pratik Sarkar // // Block-B // // Grade-7 // // Date-22/04/09 // __PROBLEM 5.5 & F.U __


 * In the ** ** following questions, use Jean's profit equation **//** P = 60t -800 **//** and your work from problem 5.2. **

A 1) In the table of data that you made in problem 5.2 what range of values did you use for the number of tune-ups?

Ans) In the table of data I made in problem 5.2, the range of values I used for the number of tune-ups was from 0 to 20.


 * 2) What range of values did you use for the profit? **

Ans) The range of values that I used for the profit was from $40 to $400 (i.e. she needs to do at least 14 tune ups to reach the break even).


 * B) Enter the profit equation into your calculator. Use the number of tune-ups as the **//** x **//** variable and the profit as the y variable. Use your answers to part A to help you decide to adjust the window setting so that you will be able to see the graph of the profit equation. Press GRAPH to display the graph. Make a sketch of the graph you see on the screen. **

Ans) ** The profit equation is ****// P= 60t – 800 //** Putting the data range of 0 to 20 in the equation, we get the following table: || Profit **(P)** in $  || ||  -800  || ||  -740  || ||  -680  || ||  -620  || ||  -560  || ||  -500  || ||  -440  || ||  -380  || ||  -320  || ||  -260  || ||  -200  || ||  -140  || ||  -80  || ||  -20  || ||  40  || ||  100  || ||  160  || ||  220  || ||  280  || ||  340  || ||  400  || Using this data, we draw the graph: //**P=60t-800**// // “P” stands for profit. //
 * No. of Tune Ups **(t)**
 * 0
 * 1
 * 2
 * 3
 * 4
 * 5
 * 6
 * 7
 * 8
 * 9
 * 10
 * 11
 * 12
 * 13
 * 14
 * 15
 * 16
 * 17
 * 18
 * 19
 * 20
 * C) How is the break-even point shown on the graph? **

Ans) From the graph we can see the profit line crosses the x-axis after the 14th. data point. This that the minimum number of tune ups required to earn a profit is 14 (which is the 15th. data point on the graph).


 * D) Look at the table of data on your calculator. How is the break-even shown on the table? **


 * Ans) **** In the table view **we can see that after completing the 13th. tune up, Jean has earned a loss of $20. Whereas when she has completed one more tune up, i.e. 14 tune ups in total, she has earned a profit of $40. This is the point when she has reached the break even (Break even is actually when the investment and total earning is equal. But in this case, there is no such data point.)

__Problem 5.5 F.U__

1) Recall that Jean wrote the equation p = 60t - 600 to represent the profit she would make if she bought used tools instead of new tools. Find an appropriate window for viewing the graph of the profit equation. Graph the equation on a calculator. Make a sketch of what you see.

Ans) ** In case Jean used the used tools in place of new tools, the profit equation would have been ** With this data, the sketch will be as below:  2) Jean wrote an equation p = 60t -1200 to represent the profit she would make if she advertised in the local paper. Find an appropriate window for viewing the graph of this profit equation. Graph this equation on a calculator. Make a sketch of what you see.
 * // P= 60t – 600 //**

Ans) ** In case Jean used the used tools in place of new tools, the profit equation would have been ** With this data, the sketch will be as below
 * // P= 60t – 1200 //**

3) Find the break even points for the equations in 1 and 2.

Ans) ** The break even point in equation 1 (P=60t-600) is the 11th. data point, i.e. after Jean completed 10 tune ups. ** ** The break even point in equation 2 (P=60t-1200) is the 21st. data point, i.e. after Jean completed 20 tune ups. **