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.

Cost and revenue can be represented as functions

The rate of change of revenue per unit is 990

The cost function from revenue is given as:

Differentiate the function with respect to time

When the change in cost per time is $9, the revenue is 1,000.

So, we have:

Make R' the subject

Divide

Multiply

Hence, the rate of change of revenue per unit is 990

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$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:

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,

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

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step-by-step explanation: