1. A private telephone company serving a small community makes a profit of *12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise per subscriber. Thus, there will be profit of 11.99 on each of the 726 subscribers. 11.98 on each 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit?
1. A private telephone company serving a small community makes a profit of *12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise per subscriber. Thus, there will be profit of 11.99 on each of the 726 subscribers. 11.98 on each 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![1. A private telephone company serving a small
community makes a profit of 12.00 per subscriber, if it
has 725 subscribers. It decides to reduce the rate by a
fixed sum for each subscriber over 725, thereby
reducing the profit by 1 paise, per subscriber. Thus,
there will be profit of 11.99 on each of the 726
subscribers. 11.98 on each 727 subscribers, etc. What
is the number of subscribers which will give the
company the maximum profit?
2. The lateral edge of a regular rectangular pyramid is a cm
long. The lateral edge makes an angle a with the plane
öf the base. Find the value of a for which the volume of
the pyramid is greatest.
3. A figure is bounded by the curves y=x+ 1, y=0, x=0
and x =. 1. At what point (a, b), a tangent should be
drawn to the curve y=:
x² +1 for it to cut off a trapezium
of the greatest area from the figure.
4. Prove that the cone of the greatest volume which can
be inscribed in a given sphere has an altitude equal to
2/3rd the diameter of the sphere.
5. Find the point at which the slope of the tangent of the
function f(x)=e cosx attains minima, when xe [0,27].
6. An electric light is placed directly over the centre of a
circular plot of lawn 100 m in diameter. Assuming that
the intensity of light varies directly as the sine of the
angle at which it strikes an illuminated surface and
inversely as the square of its distance from its surface.
How should the light be hung in order that the intensity
may be as great as possible at the circumference of the
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Transcribed Image Text:1. A private telephone company serving a small
community makes a profit of 12.00 per subscriber, if it
has 725 subscribers. It decides to reduce the rate by a
fixed sum for each subscriber over 725, thereby
reducing the profit by 1 paise, per subscriber. Thus,
there will be profit of 11.99 on each of the 726
subscribers. 11.98 on each 727 subscribers, etc. What
is the number of subscribers which will give the
company the maximum profit?
2. The lateral edge of a regular rectangular pyramid is a cm
long. The lateral edge makes an angle a with the plane
öf the base. Find the value of a for which the volume of
the pyramid is greatest.
3. A figure is bounded by the curves y=x+ 1, y=0, x=0
and x =. 1. At what point (a, b), a tangent should be
drawn to the curve y=:
x² +1 for it to cut off a trapezium
of the greatest area from the figure.
4. Prove that the cone of the greatest volume which can
be inscribed in a given sphere has an altitude equal to
2/3rd the diameter of the sphere.
5. Find the point at which the slope of the tangent of the
function f(x)=e cosx attains minima, when xe [0,27].
6. An electric light is placed directly over the centre of a
circular plot of lawn 100 m in diameter. Assuming that
the intensity of light varies directly as the sine of the
angle at which it strikes an illuminated surface and
inversely as the square of its distance from its surface.
How should the light be hung in order that the intensity
may be as great as possible at the circumference of the
pło?
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