M2L2 Quiz 2 Review M Willatt All screenshots from TI-83 Plus
In an alternate reality, let’s pretend I’m going to sew a bunch of leather purses to sell in bulk to Purses ‘R Us. I already made 25, and I have the time to make 5 more per week. Right now they would pay me $20 each, but due to increases in supply the price they would pay per piece decreases by 5¢ each week.
Purse by Kirsti I on flickr.com via CC BY SA 2.0
Technically, we could write the equation for this based on your quadratic modeling skill set from the M2L2 Notes, but instead I’ll give you the values over time and we’ll find the equation using regression on our graphing calculator: Weeks that have passed (x)
Possible Payout from Purses ‘R Us(y)
0 1 2 3 4 5 6 7 8
500 598.5 696.5 794 891 987.5 1083.5 1179 1274
Weeks that have passed (x)
Possible Payout from Purses ‘R Us(y)
0
500
1
598.5
2
696.5
3
794
4
891
5
987.5
6
1083.5
7
1179
8
1274
Just like before, you’ll go to STAT and EDIT to type in your data.
Now, you find the quadratic model using STAT and CALC
Did you choose QUADREG? If so, you should have gotten:
When graphing these, you will want to adjust your window size. Some students prefer to start with ZOOM, FIT which gives you:
Since we know a quadratic equation makes a parabola (U shape), I believe it’s going uphill to the maximum as it goes off the screen. Let’s go into WINDOW and make an educated guess as to what may work.
I usually start by changing Xmin & Ymin to a number a little below 0. Next we need to see farther right (bigger x’s) and farther up (bigger y’s) to see the rest of the “mountain” so we would increase the Xmax and Ymax until we get a nice picture. eeks w y n a That m 9 years is over
It took me a few tries until I got the window above that I liked. I changed the x scale to mark off by 100 on the axis and y scale to count by 1000. You can pick what you want.
Possible Payout from Purses ‘R Us
Number of Weeks
If I wait a while, I could sell my stock of purses for a good profit; however, if I wait too long the amount I could get for them goes back down.
I marked some important points above. Let’s find their values and interpret what they mean for my booming purse making business.
To find maximum: Press 2ND, TRACE, 4, and then move your cursor to the left of the “mountain top” & hit ENTER, move the cursor to the right of the “mountain top” & hit ENTER, and when it says “Guess?” you can just hit ENTER again.
Notice the triangles it put on the screen each time you set the cursor and hit ENTER. It will be searching between them for the maximum.
To find the y intercept: Press TRACE, 0, ENTER
To find the x intercepts: Type 0 in for Y2.
Then press 2ND, TRACE, 5 so we can find where our equation intersects height 0. You’ll need move the cursor close to one of the x intercepts and hit ENTER 3 times.
To find the other one, do the same steps, but move the cursor closer to that x intercept before hitting ENTER 3 times.
Let’s check your answers… Maximum: (197.5, 10251.6) In week 197.5, I could sell all my purses and get $10,251.60 Y intercept: (0,500) Right now (week 0), I could sell all of my purses (remember I already have 25) and get $500. X intercepts: (-5,0) & (400,0) Both of these show when I would have made $0 from selling all my purses… -5 weeks and 400 weeks. However, -5 weeks doesn’t really make sense unless I stated that negative could represent 5 weeks ago.
What about the cost of leather? We’ve never discussed how much the raw material costs me. I have locked in with my leather dealer at $20 a week to get the leather I need to make those 5 purses. If my cost is $20 a week, I would represent that as 20x. Since it takes away from the money I would receive from Purses R’ Us, we would subtract it from the equation: y = -.25(x+5)(x-400)-20x
If I regraph the new function that includes my cost‌
I would want to stop and sell all my purses at week 157.5 which would bring in $6701.56.
If I waited until week 321, I would bring in no money.