Question

If the total revenue function for a blender is R(x) = 56x − 0.01x2 where x is the number of units sold, what is the average rate of change in revenue R(x) as x increases from 11 to 22 units? $ per unit g

Answer 1

The revenue function is the sum of the profit and cost functions

The average rate of the revenue is 55.67

How to determine the average rate of change

The revenue function is given as:

$R(x) = 56x - 0.01x^2$

The interval is given as:

(a,b) =(11,22)

The average rate of change over the interval (a,b) is calculated as:

$R'(x) =\frac{R(b) - R(a)}{b -a}$

This gives

$R'(x) =\frac{R(22) - R(11)}{22 -11}$

$R'(x) =\frac{R(22) - R(11)}{11}$

Calculate R(22) and R(11)

$R(22) = 56*22 - 0.01*22^2$

$R(22) = 1227.16$

$R(11) = 56*11 - 0.01*11^2$

$R(11) = 614.79$

So, we have:

$R'(x) =\frac{R(22) - R(11)}{11}$

$R'(x) =\frac{1227.16 - 614.79}{11}$

$R'(x) =\frac{612.37}{11}$

Evaluate the quotient

$R'(x) =55.67$

Hence, the average rate of the revenue is 55.67

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