A theatre company's profit can be modeled by the function P(x) = -60x^ + 700x -1000. Where x is the price of a ticket in dollars. What is the break-even price of the tickets?
In terms of the price of the ticket x, the profit of the theater company is modeled by the function P(x) = -60x^2 + 700x -1000. At break-even the company neither makes a profit nor a loss.
-60x^2 + 700x -1000 = 0
=> 6x^2 - 70x + 100 = 0
=> 6x^2 - 60x - 10x + 100 = 0
=> 6x(x - 10) - 10(x - 10) = 0
=> (6x - 10)(x - 10) = 0
=> x = 5/3 and x = 10
When the price of the ticket is $10 and when it is $1.66 the theater company breaks even.