I need to know if I am correct...
Ques)The ticket office at Orchestra
Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x box seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income.
Ans)it will sell 50 – x box seats. The function S = 50x – x2 gives the estimated income from the sale of the box seats...
And,the maximum income S(x) is:
dS/dx = 50 - 2x = 0; x = 25
S(25) = 25 * 25 = 625
The maximum income is $625. The ticket price for that is $25.
Am I right???
yes S = 50 x - x^2
dS/dx = 0 = 50 - 2x
so
x = 25
S = 50(25) -625
= 625 sure enough
AWESOME! Thanks Damon! Are you a teacher in real life?
No, retired professor of engineering
To determine if you are correct, let's go through the steps you've outlined:
1. The function S = 50x - x^2 provides the estimated income from the sale of box seats, where x represents the price for box seats.
2. To find the price for box seats that will give the greatest income, we need to maximize the function S(x).
3. To do this, we can find the derivative of S(x) with respect to x and set it equal to zero.
dS/dx = 50 - 2x = 0
4. Solving this equation, we find x = 25 as the value that maximizes the income.
5. Finally, substitute this value back into the function S(x) to find the maximum income.
S(25) = 50(25) - (25)^2 = 625.
According to the steps you've provided, you are correct. The maximum income from the sale of box seats is $625, and the corresponding price for box seats is $25.