5 Use a spreadsheet to numerically verify the result of Exercises 1-55. For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, R ( x ) , a n d cos t , C ( x ) , a r e i n d o l l a r s f o r Exercises 23-26 Maximizing profit. Gritz-Charlston is a 300-unit luxury hotel All rooms are occupied when the hotel. Charges $80 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant Each occupied room costs $22 per day to service and maintain What should the hotel charge per day in order to maximize profit?
5 Use a spreadsheet to numerically verify the result of Exercises 1-55. For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, R ( x ) , a n d cos t , C ( x ) , a r e i n d o l l a r s f o r Exercises 23-26 Maximizing profit. Gritz-Charlston is a 300-unit luxury hotel All rooms are occupied when the hotel. Charges $80 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant Each occupied room costs $22 per day to service and maintain What should the hotel charge per day in order to maximize profit?
Solution Summary: The author explains that Gritz Charltson is a 300- unit luxury hotel and all rooms are occupied when hotel charges are 80 per day.
5 Use a spreadsheet to numerically verify the result of Exercises 1-55.
For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue,
R
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d
cos
t
,
C
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,
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Exercises 23-26
Maximizing profit. Gritz-Charlston is a 300-unit luxury hotel All rooms are occupied when the hotel. Charges $80 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant Each occupied room costs $22 per day to service and maintain What should the hotel charge per day in order to maximize profit?
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
College Algebra with Modeling & Visualization (5th Edition)
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