SOLUTION: A dreaded word problem. I can't figure this one out. The Municipal transit serves 150,000 commuters daily when the fair is $1.80. Market research has determined that every pe

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The Municipal transit serves 150,000 commuters daily when the fair is $1.80.
Market research has determined that every penny decrease in the fare will result in 1,000 new riders. What fare will maxmize revenue?
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Look at it a penny at a time and try to see the pattern:
If Fare is 180 cents the # of commuters is 150,000
If Fare is 180-1 cents the # of commuters is 150,000+1000
If Fare is 180-2 cents the # of commuters is 150,000+2(1000)
...
If Fare is 180-x cents the # of commuters is 150,000+x(1000)
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EQUATION:
Revenue = (Fare)(# of commuters)
R(x)=(180-x)(150,000+1000x)
R(x)= -1000x^2-150000x+180000x+180*150000
R(x)=-1000x^2+30000x+180*150000
Maximum occurs at x=-b/2a = -30000/-2000=15
Maximum Revenue comes when Fare = 180-15=165 cent or $1.65
Cheers,
Stan H.