MHB Calculate Flexibility of Budget Distribution: 10 & 90 vs. 50 & 50

AI Thread Summary
The discussion centers on calculating budget flexibility between two different distribution scenarios: a fixed budget of $50 for gas and $50 for entertainment versus a more flexible budget of $10 for gas and $90 for either category. The key question is how to quantify the efficiency gained from the flexible budget, as it allows for better allocation of funds based on needs. Participants emphasize the importance of defining the problem clearly to facilitate meaningful calculations. Ultimately, the goal is to determine the percentage increase in efficiency when using the flexible budget compared to the fixed one.
clock245
Messages
1
Reaction score
0
I think this is an obvious answer, but maybe I'm dense!

So not sure if this belongs in this sub-group, but let me explain my question below

Say I have a budget of $\$ 50$ for gas and $\$50$ for entertainment. I cannot cross between those two pots. So even though i have $\$ 100$ i′ve got 50% flex in terms of efficiently using my dollars.

So slightly more complicated what if i now had $\$ 10$ for gas and $\$ 90$ that could be used for gas OR entertainment? It's not really 50% flex because i am able to use my dollars more efficiently now.

How do i calculate this in a meaningful way? In other words i am X% more efficient in the $\$ 90$ and $\$ 10$ distribution vs the $\$ 50$ and $\$ 50$ distribution.

Thanks for any help you can provide.
 
Last edited by a moderator:
Mathematics news on Phys.org
clock245 said:
How do i calculate this in a meaningful way?
We can only help if you state your problem in a meaningful way...
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top