Question

Weston Publishing publishes a deluxe edition and a standard edition of its Spanish-English dictionary. Weston's management estimates that the number of deluxe editions demanded is $x$ copies/day and the number of standard editions demanded is $y$ copies/day when the unit prices are $$ \begin{array}{l} p=20-0.005 x-0.001 y \\ q=15-0.001 x-0.003 y \end{array} $$ dollars, respectively. a. Find the daily total revenue function $R(x, y)$ b. Find the domain of the function $R$

Name: Problem 41, Chapter 8: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-06-02T05:28:00-08:00
Duration: 3 min 28 s
Channel: Aman Gupta

   Weston Publishing publishes a deluxe edition and a standard edition of its Spanish-English dictionary. Weston's management estimates that the number of deluxe editions demanded is $x$
copies/day and the number of standard editions demanded is $y$ copies/day when the unit prices are
$$
\begin{array}{l}
p=20-0.005 x-0.001 y \\
q=15-0.001 x-0.003 y
\end{array}
$$
dollars, respectively.
a. Find the daily total revenue function $R(x, y)$ 
b. Find the domain of the function $R$

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 8, Problem 41

Instant Answer

Solved by Expert Aman Gupta

06/02/2021

Step 1

For the deluxe edition, the revenue is given by $R_{deluxe} = p \cdot x = (20-0.005x-0.001y) \cdot x = 20x - 0.005x^2 - 0.001xy$. For the standard edition, the revenue is given by $R_{standard} = q \cdot y = (15-0.001x-0.003y) \cdot y = 15y - 0.001xy - Show more…

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Weston Publishing publishes a deluxe edition and a standard edition of its Spanish-English dictionary. Weston's management estimates that the number of deluxe editions demanded is $x$ copies/day and the number of standard editions demanded is $y$ copies/day when the unit prices are $$ \begin{array}{l} p=20-0.005 x-0.001 y \\ q=15-0.001 x-0.003 y \end{array} $$ dollars, respectively. a. Find the daily total revenue function $R(x, y)$ b. Find the domain of the function $R$

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Key Concepts

Function Domain in Applied Contexts

The domain of a function represents the set of all input values for which the function is defined and physically meaningful. In a revenue model, this typically includes restrictions such as nonnegative demand and prices, as negative quantities or prices would be unrealistic in a business setting.

Revenue Function

A revenue function models total income by multiplying the number of units sold by their respective unit prices. In business mathematics, it often involves summing the products of various goods, each with demand-dependent prices, leaving room for further analysis such as profit maximization and cost comparison.

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