SOLUTION: The exponent Liner offers a tour package to a group of 50 persons for a price of $300 per person but it reduces the price per person by $5 for each additional person above the 50.

Question 1051969: The exponent Liner offers a tour package to a group of 50 persons for a price of $300 per person but it reduces the price per person by $5 for each additional person above the 50.
a) Does reducing the price per person to have more people join the tour give the bus company more revenue?
b) What is the maximum number of people that will give the maximum revenue for the bus company?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
300 * 50 = 15000
:
let p be the number of people > 50, then
:
15000 + (p*(300-5p) = total revenue(R)
:
1) -5p^2 +300p + 15000 = R
:
The graph of equation 1) is a parabola that curves downward, we want the coordinates of the vertex of the parabola
:
x = -b/2a = -300 / (2(-5)) = 30
:
Substitute the value of x for p in equation 1)
:
-5(30^2) +300(30) + 15000 = 19,500
:
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a) yes
:
b) max number of people is 50 + 30 = 80 people
max revenue is $19,500
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