   Chapter 12.4, Problem 7E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-12, cost, revenue, and profit are in dollars and x is the number of units.A firm knows that its marginal cost for a product is M C ¯ =   3 x   + 20 , that its marginal revenue is M R ¯ =   44   —   5 x , and that the cost of production of 80 units is $11,400.(a) Find the optimal level of production.(b) Find the profit function.(c) Find the profit or loss at the optimal level. (a) To determine To calculate: The optimal level of production where a firm has marginal cost of production MC¯=3x+20 and marginal revenue MR¯=445x and the total cost of production of 80 units is$11,400.

Explanation

Given information:

It is provided that a firm has marginal cost of production MC¯=3x+20 and marginal revenue MR¯=445x and the total cost of production of 80 units is $11,400. Formula used: Optimal Production: The optimal production occurs when marginal revenue equals to the marginal cost. MR¯=MC¯ Calculation: Consider the provided data, Marginal cost, MC¯=3x+20 and marginal revenue, MR¯=445x Consider the formula, (b) To determine To calculate: The profit function where a firm has marginal cost of production MC¯=3x+20 and marginal revenue MR¯=445x and the total cost of production of 80 units is$11,400.

(c)

To determine

To calculate: The profit and loss at optimal level where a firm has marginal cost of production is MC¯=3x+20 and marginal revenue MR¯=445x and the total cost of production of 80 units is \$11,400.

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