Question

The price-demand equation and the cost function for the production of HDTVs are given, respectively, by x = 9,000 - 30p and C(x) = 150,000 + 30x where x is the number of HDTVs that can be sold at a price of $p per TV and C(x) is the total cost (in dollars) of producing x TVs. Express the price p as a function of the demand x, and find the domain of this function.

Answer 1

The price p as a function of the demand x is given by the equation p = (9000 - x) / 30. The domain of this function, which represents all possible values for x, is 0 ≤ x ≤ 9,000. This is because x, the number of HDTVs that can be sold, can be any number from 0 up to 9,000.

Step-by-step explanation:

The price-demand equation is given by x = 9,000 - 30p. To express the price p as a function of the demand x, we can rearrange this equation to solve for p: p = (9000 - x) / 30. The domain of this function is the set of all possible values of x. In this context, x represents the number of HDTVs that can be sold, so x can be any number from 0 up to 9,000. Therefore, the domain of this function is 0 ≤ x ≤ 9,000.

Learn more about Domain of a Function