Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

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Textbook Question

Chapter 2.7, Problem 48E

Revenue, cost, and profit. The company in Problem 47 is also planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of $5,000 and variable costs of $5 per toaster.

(A) Assume that the relationship between price p and demand x is linear. Use the research department’s estimates to express p as a function of x, and find the domain of this function.
(B) Find the revenue function in terms of x and state its domain.
(C) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function in terms of x.
(D) Graph the cost function and revenue function on the same coordinate system for 0 ≤ x ≤ 800. Find the break-even points and indicate regions of loss and profit.
(E) Find the profit function in terms of x.
(F) Evaluate the marginal profit at x = 325 and x = 425 and interpret the results.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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Chapter 2.7, Problem 47E

Chapter 2.7, Problem 49E

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Chapter 2 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

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Solution Summary: The author calculates the price as a function of demand x by obtaining the domain of the function.

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