Question

The price p (in dollars) that the manufacturer of a portable digital music player is able to charge for the player is given by p=135-4x^2 where x is the number (in millions) of music players produced. It costs the company $54 to make each music player.

aWrite an expression for the company’s total revenue (in millions of dollars) in terms of x.

Answer 1

To find the expression for the company's total revenue R in terms of x, the formula used is R = x*(135-4x^2), representing the revenue gained from selling x million music players at the price dictated by the given price function p=135-4x^2.

Step-by-step explanation:

The company's total revenue is calculated by multiplying the number of units sold (x), by the price of each unit (p). In the given equation, p=135-4x2. Therefore, the expression for total revenue R, in terms of x, is found by substituting p with the given price function in the formula R = p*x, which gives us R = x*(135-4x2).

To calculate the company's total revenue in millions of dollars, we simply multiply the price function, in terms of x, by the variable x (the number of music players produced in millions). We must keep in mind that the cost to produce each unit will be excluded from the revenue calculation as it is not part of the revenue, but rather a part of the cost structure.