10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Textbook Question

Chapter 3.4, Problem 11E

MARGINAL PROFIT FOR PRODUCING LOUDSPEAKERS Refer to Exercise 10. Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be

C(x) = 200x + 300,000

a. Find the profit function P.
b. Find the marginal profit function P′
c. Compute P′ (5000) and P′ (8000).
d. Sketch the graph of the profit function, and interpret your results.

10. MARGINAL REVENUE FOR PRODUCING LOUDSPEAKERS The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand function for these speakers is

p = −0.04x + 800 (0 ≤ x ≤ 20,000)

where p denotes the speaker’s unit price (in dollars) and x denotes the quantity demanded.

a. Find the revenue function R.
b. Find the marginal revenue function R'.
c. Compute R' (5000), and interpret your results.

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Chapter 3.4, Problem 10E

Chapter 3.4, Problem 12E

Chapter 3 Solutions

APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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Solution Summary: The author calculates the profit function, which is the difference between revenue function and cost function.

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