Explanation Given information: The cost and revenue obtained after x items produced and sold is, C ( x ) = 4 x + 10 and R ( x ) = 50 x − 0.5 x 2 respectively. Where R ( x ) is revenue and C ( x ) is cost in dollars. Formula used: The concept of Max-Min Principle-2 is taken into consideration which is as follows: Suppose f is a function such that f ' ( x ) exists for every x in an interval l and there is exactly one critical value c in l , for which f ' ( c ) = 0 Then, f ( c ) is absolute maximum value over l if f ' ' ( c ) < 0 Or f ( c ) is absolute minimum value over l if f ' ' ( c ) > 0 Proof: The provided functions of revenue and cost are as follows: R ( x ) = 50 x − 0.5 x 2 C ( x ) = 4 x + 10 Subtract C ( x ) from R ( x ) , to get the profit P ( x ) : P ( x ) = R ( x ) − C ( x ) = 50 x − 0.5 x 2 − ( 4 x + 10 ) = − 0.5 x 2 + 46 x − 10 Now, first derivative of P ( x ) is, P ' ( x ) = − x + 46 The derivative exists for all values of x in [ 0 , ∞ )

Calculus and Its Applications (11th Edition)

11th Edition

ISBN: 9780321979391

Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent

Publisher: PEARSON

See similar textbooks

Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axi…

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between…

Videos

Question

Chapter 2.5, Problem 78E

To determine

To prove: The number of x units that must be produced at the cost of C(x)=4x+10 and sold at the price of R(x)=50x−0.5x2 in order to yield the maximum profit. Also calculate the maximum profit.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.5, Problem 77E

Chapter 2.5, Problem 79E

Students have asked these similar questions

Only 100% sure experts solve it correct complete solutions ok

rmine the immediate settlement for points A and B shown in figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth of foundation (DF-0), thickness of layer below footing (H)=20m. 4m B 2m 2m A 2m + 2m 4m

sy = f(x) + + + + + + + + + X 3 4 5 7 8 9 The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem and the Mean Value Theorem for f on the closed interval [0, 9] ? (A A B B C D

Chapter 2 Solutions

Calculus and Its Applications (11th Edition)

Additional Math Textbook Solutions

Find more solutions based on key concepts

Time Employed A human resources manager for a large company takes a random sample of 50 employees from the comp...

Introductory Statistics

In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...

Basic Business Statistics, Student Value Edition

CHECK POINT I You deposit $3000 in s savings account at Yourtown Bank, which has rate of 5%. Find the interest ...

Thinking Mathematically (6th Edition)

Fill in each blank so that the resulting statement is true. 1. A combination of numbers, variables, and opera...

College Algebra (7th Edition)

The table by using the given graph of h.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. St...

Elementary Statistics: Picturing the World (7th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To prove: The number of x units that must be produced at the cost of C ( x ) = 4 x + 10 and sold at the price of R ( x ) = 50 x − 0.5 x 2 in order to yield the maximum profit. Also calculate the maximum profit.

Solution Summary: The author explains how the Max-Min Principle-2 functions of revenue and cost are taken into consideration.