Question

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.

Answer 1

S=50x-x^2

dS/dx=50-2x

d2S/dx2=-2

Since acceleration is a constant negative, when velocity equals zero, it is at the absolute maximum point for S(x)...

dS/dx=0 only when 50-2x=0, 2x=50, x=25

So the price that will maximize income is $25.00 a seat.

And that maximum income is:

S(25)=50x-x^2

S(25)=$625.00

Answer 2

Answer:

$25 per box seat

Step-by-step explanation:

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