A restaurant serves between 100 and 200 people every evening. Each customer buys either the 'Meal of the Day' at $20 or the 'Gourmet Meal' at $40. No more than 25% of the customers on any evening buy the 'Gourmet Meal'. All drinks cost $5, and everybody has at least one drink, but nobody ever has more than four. On the basis of this information, what is the difference between the smallest total amount and the largest total amount customers might spend in any evening?

The answer is the second choice,  the rates at which criminals are rehabilitated into society after their sentencing

Am i first to answer?

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .