The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=28x+37,960 and R(x)=200x−0.1x2 for 0≤x≤2000. (A)Find the value of x where the graph of R(x) has a horizontal tangent line.(B)Find the profit function P(x).(C)Find the value of x where the graph of P(x) has a horizontal tangent line.(D)Graph C(x), R(x), and P(x) on the same coordinate system for0≤x≤2000.Find the break-even points. Find the x-intercepts of the graph of P(x).

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by

C(x)=28x+37,960 and R(x)=200x−0.1x² for 0≤x≤2000.

(A)	Find the value of x where the graph of R(x) has a horizontal tangent line.
(B)	Find the profit function P(x).
(C)	Find the value of x where the graph of P(x) has a horizontal tangent line.
(D)	Graph C(x), R(x), and P(x) on the same coordinate system for 0≤x≤2000. Find the break-even points. Find the x-intercepts of the graph of P(x).

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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