Answer to Question #109519 in Calculus for Naledi

Question

5. A baseball team plays in a stadium. With tickets sold at $11, the average attendance has been 27,000. They found that for every $2 decrease in ticket price the average attendance rises by 6000. Each ticket costs the team $1 per ticket. What price will maximize the profit of the baseball team?

Answer 1

We can obtain the profit of the team by the following formula: (where we decrease the price by $2x)

(27000 + 6000x)(11-2x) - (27000 + 6000x)*1 = (10 - 2x)(27000 + 6000x). After the simplifications:

profit = 2*3000(9 + 2x)(5 - x). This is the formula of parabola with the minus sign before x². This means that the maximum of this parabola is at its vertex. Using the formula for the x coordinate of the vertex, we receive x = 0.25 and the respective price equals $10.5.