Question

The demand for a new computer game can be modeled by p(x)=53−3lnx​, for 0≤x≤​800, where​ p(x) is the price consumers will​ pay, in​ dollars, and x is the number of games​ sold, in thousands. Recall that total revenue is given by R(x)=x•p(x).

a) Find R(x).

Answer 1

The total revenue function for a new video game with demand function p(x) = 53 − 3ln(x) is R(x) = 53x − 3xln(x). This represents the revenue generated from selling x thousand units of the game.

Step-by-step explanation:

The student provided demand function for new computer games is p(x) = 53 − 3ln(x), where p(x) represents the price consumers are willing to pay and x is the number of games sold in thousands. To find the total revenue function R(x), you must multiply the demand function by the quantity, giving us R(x) = x • p(x). Therefore, the revenue function can be represented as:

R(x) = x • (53 − 3ln(x)) = 53x − 3xln(x).

This function gives us the total revenue R(x) in terms of the quantity sold x. It's crucial to understand how to find and interpret the total revenue as it helps in analyzing the profitability of selling a product at various levels of output.