SOLUTION: A bus company carries about 20,000 riders for a fare of 90 cents. A survey indicates that if the fare is decreased by 5 cents, the number of riders will increase by 2,000. What pri

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A bus company carries about 20,000 riders for a fare of 90 cents. A survey indicates that if the fare is decreased by 5 cents, the number of riders will increase by 2,000. What pri      Log On


   

Question 1125541: A bus company carries about 20,000 riders for a fare of 90 cents. A survey indicates that if the fare is decreased by 5 cents, the number of riders will increase by 2,000. What price would result to the greatest revenue?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = the total revenue
Let +n+ = the number of 5 cent increases in fare
+r+=+%28+20000+%2B+2000n+%29+%2A+%28+90+-+5n+%29+
+r+=+2000%2A%28+10+%2B+n+%29%2A5%2A%28+18+-+n+%29+
+r+=+10000%2A%28+180+%2B+18n+-+10n+-+n%5E2+%29+
+r+=+10000%2A+%28+-n%5E2+%2B+8n+%2B+180+%29+
The 2nd term peaks at +n%5Bmax%5D+=+-b%2F%282a%29+
+a.=+-1+
+b+=+8+
+n%5Bmax%5D+=+-8%2F%282%2A%28-1%29%29+
+n%5Bmax%5D+=+4+
The fare/rider that maximizes revenue is
+90+-+5n+=+90+-+5%2A4+
+90+-+5n+=++70+
70 cents/rider
———————-
Here’s a plot of r/10K and n:
+graph%28+400%2C400%2C+-2%2C+20%2C+-20%2C+250%2C+-x%5E2+%2B+8x+%2B+180+%29+