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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Chapter 2.7, Problem 47E

Revenue, cost, and profit. A company is planning to manufacture and market a new two-slice electric toaster. After conducting extensive market surveys, the research department provides the following estimates: a weekly demand of 200 toasters at a price of $16 per toaster and a weekly demand of 300 toasters at a price of $14 per toaster, The financial department estimates that weekly fixed costs will be $1,400 and variable costs (cost per unit) will be $4.

(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 ≤ 1,000. 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 = 250 and x = 475 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 46E

Chapter 2.7, Problem 48E

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

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Solution Summary: The author explains the equation of a tangent line, wherein the price function is p=20-0.02x on the domain.

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