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My daughter needs serious help with Linear Programming using Graphing Calculator. She has a problem she has been trying to solve for over a month, I have tried to help her and searched endlessly for help. Hopefully, the link below works. Everything comes up fine except for the very last part. We keep getting either an Error message or 137 instead of 78, as the problem shows. Thanks in advance for any help you can provide.
https://www.dropbox.com/s/xjq0i38dz8j6j ... 1%20PM.jpg
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Linear Programming using Graphing Calculator
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Re: Linear Programming using Graphing Calculator
by Guest » Sat Nov 16, 2013 7:04 pm
Firstly it would help to know what calculator your daughter is using. Judging from the pictures I guess it's the TI-83 or something similar. I do not own such a calculator and have never used such a calculator, so I'm just guessing at what your problem is.
The example given in the image indicates a region bounded by 4 lines, Y=0, X=0, Y = (3/2)X+4, and Y = 8X-48. The objective function P = 13X+2Y will be maximized at the intersection of two of these lines. The intersections occur at (0,0) (0,4) (8,16) and (6,0) with respective objective values of 0, 8, 136, and 78.
The example doesn't cover finding the objective value at (0,0) because there is no easy way to get to it from either the lines Y1 or Y2, instead in step 5 it just notices P would be 0 so we can ignore it.
To get to to the point (0,4) you simply find where the line Y1 intersects the Y-axis. You can do this by going into the Calc menu choosing the Value option and setting X=0 for Y1. On the home screen entering 13X+2Y should give the correct objective value of 8 (as X and Y should be set to 0 and 4).
To get to to the point (8,16) you need to find where the line Y1 intersects the line Y2. You can do this by going into the Calc menu choosing the Intersect option.
To get to to the point (6,0) you need to find where the line Y2 intersects the X-axis. You can do this by going into the Calc menu choosing the Zero option (you may be asked for a left bound, right bound, and guess, maybe this is where the error is occurring).
The reason you might be getting errors or incorrect values might be that you have chosen the wrong line (i.e. you choose to find the Zero for Y1 instead of Y2). You might also need to zoom the graph out so that the Calc options work correctly (you can do this via the Zoom menu or the Window menu). You can also try entering just X or just Y for the objective function in the home screen to see what values are giving the incorrect answer of 137.
I can't really help you without further information. What exactly does your screen look like before the error, what left bound, right bound, and guess did you choose for the Zero option, what is the exact error message.
Hope this helped,
R. Baber.
The example given in the image indicates a region bounded by 4 lines, Y=0, X=0, Y = (3/2)X+4, and Y = 8X-48. The objective function P = 13X+2Y will be maximized at the intersection of two of these lines. The intersections occur at (0,0) (0,4) (8,16) and (6,0) with respective objective values of 0, 8, 136, and 78.
The example doesn't cover finding the objective value at (0,0) because there is no easy way to get to it from either the lines Y1 or Y2, instead in step 5 it just notices P would be 0 so we can ignore it.
To get to to the point (0,4) you simply find where the line Y1 intersects the Y-axis. You can do this by going into the Calc menu choosing the Value option and setting X=0 for Y1. On the home screen entering 13X+2Y should give the correct objective value of 8 (as X and Y should be set to 0 and 4).
To get to to the point (8,16) you need to find where the line Y1 intersects the line Y2. You can do this by going into the Calc menu choosing the Intersect option.
To get to to the point (6,0) you need to find where the line Y2 intersects the X-axis. You can do this by going into the Calc menu choosing the Zero option (you may be asked for a left bound, right bound, and guess, maybe this is where the error is occurring).
The reason you might be getting errors or incorrect values might be that you have chosen the wrong line (i.e. you choose to find the Zero for Y1 instead of Y2). You might also need to zoom the graph out so that the Calc options work correctly (you can do this via the Zoom menu or the Window menu). You can also try entering just X or just Y for the objective function in the home screen to see what values are giving the incorrect answer of 137.
I can't really help you without further information. What exactly does your screen look like before the error, what left bound, right bound, and guess did you choose for the Zero option, what is the exact error message.
Hope this helped,
R. Baber.
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