MHB Linear Programming using Graphing Calculator

AI Thread Summary
The discussion focuses on a linear programming problem that a user’s daughter has been struggling with for over a month while using a graphing calculator. The user reports receiving an error message or an incorrect result of 137 instead of the expected 78. Another participant clarifies that the correct answer of 78 is derived from the bottom right corner of the double shaded region in the graph, where the line intersects at X=6 and Y=0. This participant explains that the objective function evaluates to 78 when substituting these values. The conversation emphasizes the importance of understanding the graph and calculations to resolve the issue.
safaulk
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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/xjq0i38dz8j6jeh/Photo Nov 16, 1 05 11 PM.jpg
 
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Welcome to the forum.

I can't help you with using the calculator (perhaps somebody else on this forum can), but I can explain why the answer is 136, as the linked picture says. If you are getting 137, that's pretty close to the correct result. Why are you saying that you are expected to get 78?

For starters, here are the relevant graphs (the picture is clickable).

[GRAPH]00wufkkqgc[/GRAPH]

Please let me know if you need help of this sort.
 
safaulk said:
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/xjq0i38dz8j6jeh/Photo Nov 16, 1 05 11 PM.jpg

I suspect your daughter is calculating something different from what was intended.
Let me try and explain the reason for the answer 78 and perhaps it will help you two to figure out what whent wrong.

The answer 78 should come out for the bottom right corner of the double shaded region.
This is where the line $Y=8X-48$ has its ZERO ($Y = 0$).
In other words, where $8X-48 = 0$.
The corresponding $X = 6$.
So the bottom right corner is at $X = 6$ and $Y = 0$.

The objective function in the bottom right corner is
$$13X + 2Y = 13 \times 6 + 2 \times 0 = 78$$
 

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