example 7 Marginal Revenue and Marginal Profit

Chapter 1.3

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

b. Find the profit function.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

2009 PBLPathways

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The slope is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The slope is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The slope is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The slope is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The rate is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The rate is 89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The rate is 89.50

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

The rate is 89.50

1 unit

$89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

a. What is the marginal revenue for this product, and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 89.50 0R x x

m x b

89.50 0m b

An increase in production of 1 unit corresponds to an increase in revenue of $89.50

1 unit

$89.50

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

b. Find the profit function.

( ) 89.50R x x( ) 54.36 6790C x x

profit revenue cost

( ) ( ) ( )

89.50 54.36 6790

89.50 54.36 6790

35.14 6790

P x R x C x

x x

x x

x

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

2009 PBLPathways

A company produces and sells a product with revenue given by dollars and cost given by dollars where x is the number of units produced.

c. What is the marginal profit for this product and what does it mean?

( ) 89.50R x x( ) 54.36 6790C x x

( ) 35.14 6790P x x

m x b

35.14 6790m b

35.14 dollarsrate

1 unit

An increase in production of 1 unit corresponds to an increase in profit of $35.14