Question

A company knows that unit cost C and unit revenue R from the production and sale of x units are related by Upper C equals StartFraction Upper R squared Over 220 comma 000 EndFraction plus 3221.C= R2 220,000+3221. Find the rate of change of revenue per unit when the cost per unit is changing by $ 9$9 and the revenue is ​$1 comma 0001,000.

Answer 1

Answer:

$990 per unit.

Step-by-step explanation:

The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:

$C=\dfrac{R^2}{220000} +3221$

We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is ​$1,000.

Rate of Change of C,

$\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\ 9, R=\ 1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\ 990 per unit$

The Revenue is changing at a rate of $990 per unit.