Chapter 10.3, Problem 29E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

A firm can produce only 1000 units per month. The monthly total cost is given by
*x* is the number produced. If the total revenue is given by
*x*, should the firm produce for maximum profit? Find the maximum profit.

To determine

**To calculate:** The maximum profit of the provided cost function

Explanation

**Given Information:**

The provided cost function is:

And the revenue function is:

**Formula used:**

If

And,

Where,

If

To evaluate the relative maxima and minima of a function,

Step 1: Evaluate the critical values of the function.

Step 2: Now substitute the critical values into

Step 3: Evaluate

If *a*.

If *a*.

If

**Calculation:**

Consider the provided cost function:

And provided revenue function:

Profit function can be written as:

Put provided values of cost and the revenue functions:

The absolute maxima and absolute minima will occur only at the critical points.

To calculate the critical points of the profit function find the first derivative of the function:

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