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The demand for a new computer game can be modeled by p(x) = 53.5-81nx, where p(x) is the price consumers will pay, in dollars and x is the number of games sold, in thousands. Recall that total revenue is given by R(x)=x- p(x) a) Find the marginal revenue, R'(x). b) How many games will be sold if the price is $40?

The demand for a new computer game can be modeled by p(x) = 53.5-81nx, where p(x) is the price consumers will pay, in dollars and x is the number of games sold, in thousands. Recall that total revenue is given by R(x)=x- p(x) a) Find the marginal revenue, R'(x). b) How many games will be sold if the price is $40?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematical Modeling of Game Demand and Revenue** The demand for a new computer game can be modeled by the equation \( p(x) = 53.5 - 8 \ln x \), where \( p(x) \) represents the price consumers are willing to pay, measured in dollars, and \( x \) represents the quantity of games sold, measured in thousands. The total revenue \( R(x) \) is calculated by the formula: \[ R(x) = x \cdot p(x) \] ### Tasks: a) **Find the Marginal Revenue, \( R'(x) \).** b) **Determine the Number of Games Sold if the Price is $40.**
Transcribed Image Text:**Mathematical Modeling of Game Demand and Revenue** The demand for a new computer game can be modeled by the equation \( p(x) = 53.5 - 8 \ln x \), where \( p(x) \) represents the price consumers are willing to pay, measured in dollars, and \( x \) represents the quantity of games sold, measured in thousands. The total revenue \( R(x) \) is calculated by the formula: \[ R(x) = x \cdot p(x) \] ### Tasks: a) **Find the Marginal Revenue, \( R'(x) \).** b) **Determine the Number of Games Sold if the Price is $40.**
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Step 1: Find revenue function.

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