SOLUTION: 6. A bus charter company offers a travel club the following ar- rangements: If no more than 100 people on a certain tour, the cost will be $500 per person, but the cost per person

Question 1046448: 6. A bus charter company offers a travel club the following ar- rangements: If no more than 100 people on a certain tour, the cost will be $500 per person, but the cost per person will be reduced by $4 for each person in excess of 100 who takes the tour.
a. Express the total revenue R obtained by the charter com pany as a function of the number of people who go on the tour,
b. Sketch the graph of R. Estimate the number of people that results in the greatest total revenue for the charter company.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
6. A bus charter company offers a travel club the following ar- rangements: If no more than 100 people on a certain tour, the cost will be $500 per person, but the cost per person will be reduced by $4 for each person in excess of 100 who takes the tour.
:
let x = no. persons in excess of 100
x also = no. of $4 reductions in cost per person
:
a. Express the total revenue R obtained by the charter company as a function of the number of people who go on the tour,
R(x) = (100+x)(500-4x)
FOIL
R(x) = 50000 - 400x + 500x - 4x^2
R(x) = -4x^2 + 100x + 50000
:
b. Sketch the graph of R.
y = total revenue
x = no. of persons over 100
Graph: y = -4x^2 + 100x + 50000

:
Estimate the number of people that results in the greatest total revenue for the charter company.
It looks like the max revenue occurs when x=12, so 112 persons for max rev
that would be 112 * 452 = $50,624
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