SOLUTION: a charter company will provide a plane for a fare of $200 each for 80 or fewer passengers. For each passenger in excess of 80, the fare decreases $2 per person for everyone. What

Question 254415: a charter company will provide a plane for a fare of $200 each for 80 or fewer passengers. For each passenger in excess of 80, the fare decreases $2 per person for everyone. What number of passengers would produce for the greatest revenue for the company?
That is question I need to solve, but what I really need is an equation to use to solve this.
If so, can you show me how to do step by step?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
P = (80+x)(200-2x)
P = is a parabola that opens down. This means there is a maximum profit somewhere.
P = -2x^2 + 40x + 16000
We can find the vertex using -b/2a as
-b/2a = (-40/-4) = 10
Put in x = 10 and we get
P = 90*180 = 16200
Since the number of passengers increases, we get 80+10 = 90.
90 passengers gives us a profit of $16,200
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