List of quantitative methods for optimization

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The discussion centers on optimizing the linear programming problem defined by the objective function Max: 3x + 5y with specific constraints. The simplex method yields a maximum profit of $14, which can be increased to $19 by adjusting the right-hand side (RHS) of the first constraint from 5 to 7. Participants are asked to suggest additional quantitative methods, like sensitivity analysis, that can further enhance profit. There is a clarification that the maximum profit under the current constraints is indeed $14, indicating that any changes should be carefully considered. The conversation highlights the importance of exploring various optimization techniques to improve profitability.
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Max: 3x + 5y
s.t. x + 2y ≤ 5
x ≤ 3
y ≤ 2
x,y ≥0

By the simplex method, the profit is $14. Using sensitivity analysis I changed the RHS of the 1st constraint and keeping everything else constant, I get the best profit value of $19 at RHS of 7.

What other methods can I use such as the sensitivity analysis to see the improvement in my profit? Please provide me with a list.

Thanks
 
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The improvement in profit if you change what? With the given constraints, 14 is clearly the maximum.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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