Algebra
posted by Steve on .
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=(50025x)(2+0.25x) Use vertex form to find how the vendor can maximize her daily revenue.

Don't see much trig here.
R = (50025x)(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(x6)^2  600
So, the max occurs where x = 6
R(6) = 1225 when dogs cost $2 + 6*.25 = $3.50 
R=(50025x)(2+0.25x)