Final answer:
To calculate total revenue, the company should multiply the price function p(x) by the sales function s(x). This operation yields the total revenue function R(x) = p(x) × s(x), which represents the total income from video game sales at any given point in time since the company started producing games.
Step-by-step explanation:
To find the total revenue from their video games, a company that makes video games and has price and sales functions given by p(x) = 30x + 2 and s(x) = 500x + 250 respectively, should use the operation of multiplication on the polynomials. The total revenue at any point in time is the product of the price of a video game and the number of video games sold. Therefore, the total revenue function, R(x), is obtained by multiplying the price function, p(x), by the sales function, s(x), which results in R(x) = p(x) × s(x).
To illustrate, if the company wants to calculate the total revenue for a particular year since they started making games, they would substitute that year into the value of x and solve for R(x). For example, if the company has been making games for 5 years, the total revenue would be R(5) = (30 × 5 + 2) × (500 × 5 + 250), which simplifies to R(5) = (152) × (2750), giving the total revenue generated in the fifth year.