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March 24, 2017

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algebra 2 trig: A food vendor at a stadium sells hot dogs for $2. At this price, she can sell about 500 hot dogs per day. For every $.25 increase in price, she will sell 25 less hot dogs. The vendor's revenue can be modeled by R=(500-25x)(2+0.25x) Use vertex form to find how the vendor can maximize her daily revenue.

  • Algebra - ,

    Don't see much trig here.

    R = (500-25x)(2+.25x)
    = 1000 + 125x - 50x - 6.25x^2
    = 1000 + 75x - 6.25x^2
    R = -6.25(x^2 - 12x - 160)
    = -6.25(x^2 - 12x + 36 - 160 - 36)
    = -6.25(x-6)^2 - 600

    So, the max occurs where x = 6
    R(6) = 1225 when dogs cost $2 + 6*.25 = $3.50

  • Algebra - ,

    R=(500-25x)(2+0.25x)

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