Inequalites

I drew the region. 1st, I am sure that you know that one of the points is not (42, 128) but it is rather (300/7, 900/7).

Can you please tell me what you found for P for the 3 points. We will go from there once you post your results.
 
amathproblemthatneedsolve said:
https://www.desmos.com/calculator/xgjplwwwpn Heres the shaded graph. For P I found( labeling point A(0,300) B(75,225) and C (300/7, 900/7))
A and B are both $2250 while C is not even near. So for maximum profit use either point A or B where A has 0 children tickets and 300 adult while point B remains the same at 75 children and 225adults.
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Why does the answer have to be one of the vertices? Why not anything along that edge?
 
Jomo said:
I looked at your updated graph which does NOT show the feasible region. With all those shaded regions how did YOU know which region to check for the max P? Just curious.
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Desmos unlike most shades in the feasible area just look where all colors overlap
 
amathproblemthatneedsolve said:
Don't maximums and minimums occur as vertexs?
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Yes, that is why I suggested that you check just the vertices. But in some cases you can also obtain the SAME max (or min) on one of the edges.
One edge on the feasible solution set came from the line x+y=300. The slope of that line segment is m=-1. Now what is the slope of the function which you want to maximize. Considering P as a constant, the slope of the line P= 7.5x + 7.5y is also m=-1. So any point on the line x+y=300 IN THE FEASIBLE REGION will also yield a max (same max as you found!). So (1,299), (3,297), (5,295) are also solutions.
 
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