Mathematics

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.

2 Answer

  • 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:

    $25 per box seat

    Step-by-step explanation:

    I took the exam

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