Chapter 10.3, Problem 30E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

A firm can produce 100 units per week. If its total cost function is
*x,* should it produce to maximize its 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 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

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