Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

downward opening parabola,find max revenue without algebra or calculus

Ticket prices are going up and # of passengers riding daily are going down
with these 2 simple statements.  I will show an easy short-cut
way of getting the 15 unit answer of $10 per unit we should raise the ticket
price from $100 to $250.

# of people riding = 2000 - 50*unit
Price of ticket = $100 + $10 * unit

Okay instead of multiplying and getting a downward parabola and getting the maxima,
here is a FuN method I just discovered that just plays with ratios.
Attempt to get the amount added and the amount subtracted equal or same numbers.
Then find the middle of the two numbers for ticket and people...
2000 - 50
    100 + 10
200 - 5
400 - 10
Now both add or subtract 10.  Cool!
So 250 is the average of 100 and 400, and it takes 15 units of the plus or minus 10 to reach the 250 number
from either expression.
And that's it!!   That is the actual answer you get!
Alternatively,
2000 - 50 * units
    100 + 10 * units
200 - 5 * units
    10 + 1 * units
40 - 1 * units
Now both are subtracting by single "1" units...
So find middle of 10 and 40, which is 25, and that is 15 units from 40 or 10,
so we again raise the ticket cost by $10 times 15, or raise the cost by $150.
Yeehah!!

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