A tour operator believes the profit P, in dollars, from selling x tickets is given by Using this model, what is the maximum profit the tour operator can expect?
A) $6912
B) $96
C) $2304
D) $2303
E) $2300

Question

A tour operator believes the profit P, in dollars, from selling x tickets is given by  Using this model, what is the maximum profit the tour operator can expect?
A) $6912 
B) $96 
C) $2304 
D) $2303 
E) $2300

Quizplus · Accepted Answer

To find the maximum profit, we need to find the vertex of the quadratic function. The vertex of a quadratic function in the form of y = ax² + bx + c is given by (-b/2a, f(-b/2a)).
For this function, a = -0.02, b = 120, and c = 600. Plugging into the formula, we get (-b/2a, f(-b/2a)) = (-120/(-0.04), f(1500)), where we used the formula x = -b/2a and x = 1500 (halfway between the given domain values of 1000 and 2000).

Now we just need to plug in x = 1500 into the profit equation to find the maximum profit:
P(1500) = -0.02(1500)² + 120(1500) + 600 = $2304.

Therefore, the maximum profit the tour operator can expect is $2304, which is answer choice C.

A Tour Operator Believes the Profit P, in Dollars, from Selling