Question

A single rose street vendor has found that the number of roses he sells in a day depends on the price charged per rose. The more the vendor charges for a rose, the fewer people decide to purchase one. The function p(x)=2.00+0.50x represents price charged per rose where x is the number of $0.50 increases he changes over a price of $2.00 per rose. The function f(x)=80-2x represents the number of customers expected to purchase a rose where x is the number of $0.50 increases charged per rose over a price of $2.00 per rose. What does (p*r)(x) represent in the context of the situation? A. (p*r)(x) represents the revenue from selling r(x) roses at a cost of p(x) per rose B. (p*r)(x) represents the profit from selling r(x) roses at a cost of p(x) per rose. C. (p*r)(x) represents the profit from selling p(x)) roses at a cost of r(x) per rose D. (p*r)(x) represents the revenue from selling p(x) roses at a cost of r(x) per rose

Answer 1

The product of the price function p(x) and the number of roses sold function r(x), given as (p*r)(x), represents the total revenue generated from selling r(x) roses at p(x) per rose.

Step-by-step explanation:

In the given scenario, the function p(x) = 2.00 + 0.50x represents the price charged per rose, and the function f(x) = 80 - 2x represents the number of customers expected to purchase a rose. If we consider r(x) as another way of referring to the function f(x), which denotes the number of roses sold, then the product of these two functions, (p*r)(x), would represent the total revenue generated from selling r(x) roses at a cost of p(x) per rose. This corresponds to option A in the provided choices, as it captures the total income before costs are subtracted.