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.
:
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
{{{ graph( 300, 200, -50, 100, -10000, 60000, -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