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**ione** let x be the quantity of hot dogs sold

let p(x) be the price function

let R(x) be the revenue function

The stadium vending company finds that sales of hot dogs average 34000 hot dogs per game when the hot dogs sell for $2.50 each so p(x) has the ordered pair (34000, 2.50)

For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs so p(x) has slope .50/-5000

So p(x) - 2.50 = -.50/5000 (x - 34000)

Solve for p(x) then find R(x)=xp(x)

You can find the value of x that gives the maximum revenue by finding the derivative of R(x), setting it equal to zero and solving for x. If the derivative of R(x) changes from positive to negative at that value of x, you know that R(x) is maximum at that value of x.