Question

A frozen yogurt vendor has found that the number of frozen yogurts he sells in a day depends on the price charged per frozen yogurt. The more the vendor charges for a frozen yogurt, the fewer people decide to purchase one. The function p(x)=4.00+0.75x represents price charged per rose where x is the number of $0.75 increases he charges over a price of $4.00 per frozen yogurt. The function f(x)=120−4x represents the number of customers expected to purchase a frozen yogurt, where x is the number of $0.75 increases charged per frozen yogurt over a price of $4.00 per frozen yogurt. What does (f⋅p)(x) represent in the context of the situation?

Answers:
(f⋅p)(x) represents the reveunue selling f(x) frozen yogurts at a price of p(x) per yogurt.

(f⋅p)(x) represents the revenue selling p(x) frozen yogurts at a price of f(x) per yogurt.

(f⋅p)(x) represents the cost of selling p(x) frozen yogurts at a price of f(x) per yogurt.

(f⋅p)(x) represents the cost of selling f(x) frozen yogurts at a price of p(x) per yogurt.

Answer 1

The function f(x) * p(x) represents the revenue from selling f(x) frozen yogurts at the price p(x) per yogurt. (First option)

Explanation:

Recall that the revenue is defined as the product of the price per object sold times the number of sales. In our case, the price per object (frozen yogurt) is given by p(x), and f(x) represents the number of customers that are expected to purchase frozen yogurt according to the number of "x" $0.75 increases over $4. This is clearly a problem of "increase-decrease" where as the variable x increases (number of $0.75 increases), one of the functions decreases (in this case the number of possible sales), while the other function increases (in this case the actual price per yogurt).

Therefore, the product of the two functions represents the total revenue from selling f(x) frozen yogurts at a price p(x) per yogurt. This coincides with the first option given among the listed answers.