What would be the answer for the constant proportionality?

a community theater currently sells 200 season ticket at $50 each.

in order to increase its season ticket revenue without increasing the number of season tickets that it sells, the theater surveys its season ticket holders to see if they would be willing to pay more.

the survey finds that for every $5 increase in the price of a ticket the theater would lose 10 season ticket holders.

what function if any, should the theater take to increase revenue?

:

Let x = the number of $5 increases and the number of 10 ticket decreases

Write an equation to find the revenue for this situation

R(x) = (200 - 10x)*(50 + 5x)

FOIL

R(x) = 10000 + 1000x - 500x - 50x^2

R(x) = -50x^2 + 500x + 10000 is the function

:

Max revenue occurs at the axis of symmetry, use x = -b/(2a) to find that

x = %28-500%29%2F%282%2A-50%29

x = +5 ea $5 increases so $75 will give max revenue (you lose 50 ticket holders)

:

Actual Revenue then: 75 * 150 = $11,250 vs 50 * 200 = $10000 originally

Step-by-step explanation:

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