The revenue in thousands of dollars from producing x units o

The revenue (in thousands of dollars) from producing x units of an item is modeled by R (x)=10x-0.01x²

A. Find the average rate of chage in revenue as x changes from 1003 to 1008

B. Find the marginal revenue at x=400.

Solution

R (x)=10x-0.01x²

average rate of change of revenue =[R(1008)-R(1003)]/(1008-1003)

average rate of change of revenue =[(10(1008)-0.01(1008)²)-(10(1003)-0.01(1003)²)]/(1008-1003)

average rate of change of revenue =[(10(1008)-10(1003) -0.01(1008)²+0.01(1003)²)]/(1008-1003)

average rate of change of revenue =[(10(1008-1003) -0.01(1008 ²-1003²)]/(1008-1003)

average rate of change of revenue =[(10(1008-1003) -0.01(1008 -1003)(1008+1003)]/(1008-1003)

average rate of change of revenue =[10 -0.01(1008+1003)]

average rate of change of revenue =[10 -20.11]

average rate of change of revenue -10.11 $/ unit

B)

marginal revenue =dR/dx =10 -0.02x

x =400

dR/dx =10 -0.02*400

dR/dx =2

marginal revenue =2 $/unit