Chapter 10, Problem 15T

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

A firm sells 100 TVs per month at $300 each, but market research indicates that it can sell 1 more TV per month for each $2 reduction of the price. At what price will the revenue be maximized?

To determine

**To calculate:** The price at which TV should be sold to maximize the revenue where the firm sells

Explanation

**Given Information:**

The firm sells per month 100 TV and it can sell one more at

**Formula used:**

To find relative maxima and minima of a function,

1. Set the first derivative of the function to zero,

2. Substitute the critical values into

3. Calculate the sign of the function to the left and right of the critical values.

(a) If

(b) If

**Calculation:**

Consider a firm sells

Let *x* represent the additional units of TV sold by the firm.

Since, the number of units sold is

Then, revenue is the product of number of units sold and the price.

Thus, the revenue function is given by

Calculate the first derivative of the function

Set the first derivative equal to 0.

Solve for *x*.

Now, calculate the values of the first derivative on either side of the critical point

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