Question 1108140
profit = revenue minus cost.


revenue is 5 dollars a ticket plus 1400 dollars in concessions.


the cost for the players is 2000 dollars and the cost for the other workers is 1600.


each person who buys a tickets gets a free bat that costs 3 dollars each.


let x equal the number of people who buy a ticket.


revenue = 1400 + 5x.


that's the revenue from the concessions plus 5 dollars for each ticket sold.



cost = 3600 + 3x


that's 2000 for the players and 1600 for the workers and 3 dollars for each bat given away.


profit = revenue minus cost.


profit = 1400 + 5x - (3600 + 3x)


simplify to get:


profit = 1400 + 5x - 3600 - 3x.


combine like terms to get:


profit = -2200 + 2x.


to find the break even point, set profit equal to 0.


set p = 0 and the profit equation becomes:


0 = -2200 + 2x.


add 2200 to both sides of this equation to get:


2200 = 2x


divide both sides of this equation by 2 to get:


1100 = x


they will  break even when the number of tickets sold is 1100.
to make a profit, they have to sell more than 1100.
to take a loss, they have to sell less than 1100.


profit equation is, once again:


p = -2200 + 2x


when x = 1100, the equation becomes:


p = -2200 + 2*1100 which becomes p = -2200 + 2200 which becomes p = 0.


they didn't take a loss, but they didn't make a profit either.


when x > 1100, like say 1200, the equation becomes:


p = -2200 + 2 * 1200 which becomes p = -2200 + 2400 which becomes p = 200.


now they've made a profit of 200 dollars if they sold 1200 tickets.


make x < 1100, like say 800, the equation becomes:


p = -2200 + 2 * 800 which becomes p = -2200 + 1600 which becomes p = -600.


negative profit is a positive loss, therefore they took a loss of 600 if they only sold 800 tickets.


let's look at the profit equation when they sold 1200 tickets and break it down into its revenue and cost components.


p = -2200 + 2 * x becomes p = -2200 + 2400 which becomes p = 200.


revenue is 1400 + 5*1200 = 1400 + 6000 = 7400.
cost is 3600 + 3*1200 = 3600 + 3600 = 7200.
profit is revenue minus cost = 7400 - 7200 = 200.