Let n: # of $2/ticket price increases price/ticket: (12 + 2n) ticket buyers: 26,000 - 6,000n
R(n): revenue (in $) as a function of n
R(n) = (12 + 2n)(26,000 - 6,000n)
At this point it should be elementary to FOIL, take the derivative using power rule, set R' = 0 and solve for the ideal n. However, simple precalculus or even Algebra 2 can be used in this way: R(n) a concave down parabola in factored form with zeros at n = - 6 and n = 4.333. The average of these is -5/6, so the axis of symmetry is n = -5/6, meaning the vertex (aka maximum) for the Revenue function lies on n = -5/6. Assuming only integer numbers of price hikes are possible, n = -1, and the ideal ticket price is $10/ticket.
