the revenue from selling movie tickets is given by the function r(t) = 10t, where \t\ is the number of…

the revenue from selling movie tickets is given by the function r(t) = 10t, where \t\ is the number of tickets sold. the theater holds a maximum of 200 people. the profit is a function of the revenue \r\ and is given by the function p(r) = 0.20r. what is the domain of the profit function p(r)?\na {0, 1, 2, 3, ... , 200}\nb {0, 10, 20, 30, ... , 2000}\nc {any nonnegative real number ≤ 200}\nd {any nonnegative real number ≤ 2000}

the revenue from selling movie tickets is given by the function r(t) = 10t, where \t\ is the number of tickets sold. the theater holds a maximum of 200 people. the profit is a function of the revenue \r\ and is given by the function p(r) = 0.20r. what is the domain of the profit function p(r)?\na {0, 1, 2, 3, ... , 200}\nb {0, 10, 20, 30, ... , 2000}\nc {any nonnegative real number ≤ 200}\nd {any nonnegative real number ≤ 2000}

Answer

Explanation:

Step1: Find the range of ticket - sales

The number of tickets $t$ sold satisfies $0\leq t\leq200$ since the theater holds a maximum of 200 people and the number of tickets cannot be negative.

Step2: Find the range of revenue

The revenue function is $R(t) = 10t$. When $t = 0$, $R(0)=10\times0 = 0$; when $t = 200$, $R(200)=10\times200=2000$. So, $0\leq R\leq2000$.

Step3: Determine the domain of the profit function

The profit function $P(R)$ is a function of revenue $R$. Since $R$ (the input to $P(R)$) ranges from $0$ to $2000$ and $R$ can be any non - negative real number in this interval, the domain of $P(R)$ is any non - negative real number $\leq2000$.

Answer:

D. {any non - negative real number $\leq2000$}