A supermarket sells two brands of coffee: brand A at p per...

A supermarket sells two brands of coffee: brand $A$ at $\$ p$ per pound and brand $B$ at $\$ q$ per pound. The daily demand equations for brands $A$ and $B$ are, respectively, $$ \begin{array}{l} x=200-5 p+4 q \\ y=300+2 p-4 q \end{array} $$ (both in pounds). Find the daily revenue function $R(p, q)$ Evaluate $R(2,3)$ and $R(3,2)$

A supermarket sells two brands of coffee: brand $A$ at $\$ p$ per pound and brand $B$ at $\$ q$ per pound. The daily demand equations for brands $A$ and $B$ are, respectively,
$$
\begin{array}{l}
x=200-5 p+4 q \\
y=300+2 p-4 q
\end{array}
$$
(both in pounds). Find the daily revenue function $R(p, q)$ Evaluate $R(2,3)$ and $R(3,2)$

Key Concepts

Function Evaluation

Function evaluation is the process of substituting specific values for the variables in a function to compute a numerical result. This step is crucial in applying theoretical models to real-world scenarios by finding the actual output for given input values.

Substitution in Functions

Substitution involves replacing variables in one function with another expression, which is essential when one needs to combine different functions. This technique is particularly useful when integrating demand functions into a revenue function to create a comprehensive model.

Revenue Function

A revenue function represents total income generated by selling goods or services, and it is typically defined as the product of price and quantity sold. In economic problems, it is used to model how changes in price affect the earnings from sales.

Demand Function

A demand function shows the relationship between the price of a product and the quantity demanded by consumers. These functions can depend on various factors, including the product's own price and the price of related goods, and they are key in determining market behavior.

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