A hotel rents 240 240 rooms at a rate of $ 40 $40 per day. For each $ 2 $2 increase in the rate, four fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $

Answers

Answer 1

Answer:

The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600

Step-by-step explanation:

Given

[tex]Rooms = 240[/tex]

[tex]Price= \$40[/tex]

[tex]Increment = \$2[/tex]

First, we calculate the revenue.

[tex]Revenue (r) = Price (p) * Number\ of\ Rooms(n)[/tex]

[tex]r = p*n[/tex]

Let x be the change in rate.

i.e.

For every 2x increment in price (p) i.e. p + 2x

There will be 4 fewer rooms (n) i.e. n - 4x

So, the revenue is updated as:

[tex]r = (p + 2x) * (n - 4x)[/tex]

[tex]Price = 40[/tex]

So:

[tex]r = (40 + 2x) * (n - 4x)[/tex]

[tex]Rooms = 240[/tex]

So:

[tex]r = (40 + 2x) * (240 - 4x)[/tex]

Expand

[tex]r = 40 * 240 - 40 * 4x + 2x * 240 - 2x*4x[/tex]

[tex]r = 9600 - 160x + 480x - 8x^2[/tex]

Reorder

[tex]r = -8x^2 - 160x + 480x + 9600[/tex]

[tex]r = -8x^2 +320x + 9600[/tex]

The maximum of a function is calculated as:

[tex]Max = -\frac{b}{2a}[/tex]

In: [tex]r = -8x^2 +320x + 9600[/tex]

[tex]a = -8[/tex]   [tex]b = 320[/tex]    [tex]c = 9600[/tex]

So:

[tex]Max = -\frac{b}{2a}[/tex]

[tex]Max = -\frac{320}{-8}[/tex]

[tex]Max = \frac{320}{8}[/tex]

[tex]Max = 40[/tex]

To get the maximum revenue;

Substitute 40 for x in [tex]r = -8x^2 +320x + 9600[/tex]

[tex]r = -8(40)^2 + 320 * 40 + 9600[/tex]

[tex]r = 9600[/tex]

The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600


Related Questions

fill in the blank:
5/7 of ... is 1/7

Answers

5/49

Hope this helps!! :)

Answer: 1/3

5/7 x X=1/7 35x= 7

X=7/35 simplified version 1/3

(HELP ME )Jolie played dodgeball in PE. In one game, Jolie threw a total of 75 balls at her
opponents in one day of dodgeball. She hit 30 of her opponents. What percent of her
targets did she hit?

Answers

Answer:

40%

Step-by-step explanation:

A percent is;

[tex]\frac{part}{whole} = \frac{x}{100}[/tex]

It is given that Jolie the 75 dodgeballs in total, hence the whole is 75. It is also given that 30 of the dodgeballs hit the target, so the part is 30. Now all one has to do is solve for "x".

[tex]\frac{30}{75} = \frac{x}{100}[/tex]

Simplify [tex]\frac{30}{75}[/tex] by dividing the numerator and denominator by 15.

[tex]\frac{2}{5}[/tex]

Now the equation is;

[tex]\frac{2}{5}=\frac{x}{100}[/tex]

Typically, one would solve a proportion by doing cross products, but in this case, it is easier to think about it intuitively. Since 5 is a factor of 100 (5 * 20 = 100), then all one has to do is multiply [tex]\frac{2}{5}[/tex] by 20 to get the answer (on the numerator).

x = 40

Answer:

40%

Step-by-step explanation:

30/75 = 0.40

0.40*100 = 40

75 * 40% = 30

Addison has 124,234,281,284 cartons of milk, she dropped like 456,789,098,345,678,987,654,568 of them, how many did bruh bruh bruh 21 haha lebron james

Answers

Answer:

Lebron James = bruh bruh bruh

Step-by-step explanation:

Answer:

Lol free points

Step-by-step explanation:

I need help finding the slope, identifying the initial value and writing An equation for a linear function and finding the X answer Y intercept PLEASE HELP PLEASE ​

Answers

Answer/Step-by-step explanation:

✔️Slope (m) using the two points (2, 4.58) and (5, 4.28):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4.28 - 4.58}{5 - 2} = \frac{-0.3}{3} = -0.1 [/tex]

Slope (m) = -0.1

✔️Initial Value = y-intercept = b

To find b, substitute x = 2, y = 4.58, and m = -0.1 into y = mx + b.

(Note: y is P(t) and x is t).

Thus:

4.58 = (-0.1)(2) + b

4.58 = -0.2 + b

Add 0.2 to both sides

4.58 + 0.2 = b

4.78 = b

b = 4.78

Initial value = 4.78

✔️Equation for the linear function:

Substitute b = 4.78, and m = -0.1 into P(t) = mt + b

Thus the equation would be:

P(t) = -0.1t + 4.78

✔️The y-intercept = initial value = 4.78

✔️The x-intercept = the value of t when P(t) = 0.

To get this, substitute P(t) = 0 into P(t) = -0.1t + 4.78.

Thus:

0 = -0.1t + 4.78

Add 0.1t to each side

0.1t = 4.78

Divide both sides by 0.1

t = 47.8

x-intercept = 47.8

3(x + 1) + 2(x + 5)
Whats the answer to this

Answers

Let's simplify step-by-step.

3(x+1)+2(x+5)

Distribute:

=(3)(x)+(3)(1)+(2)(x)+(2)(5)

=3x+3+2x+10

Combine Like Terms:

=3x+3+2x+10

=(3x+2x)+(3+10)

=5x+13

PLEASE HELPPPPPPP

Arun ran without stopping, which is closest to the benchmark fraction ___. On Tuesday, he ran 7/15 without stopping, which is the closest benchmark fraction ___. Arun ran about ____ mile(s) over the two days.
A. 1/2, 1/2, 1
B 1/4, 1/2, 3/4
C. 0/4,3/4,3/4​​

Answers

Answer:

Option C is correct answer

Can you Simplify
5a - a

Answers

Answer:

4a is the answer.

Step-by-step explanation:

5a - a

= 4a

Answer:

It is 4a.

Step-by-step explanation:

=5a-a

=4a

Hope it helps you..

10 (1/2x+2)-5=3(x-6)+1

Answers

Answer:

x = -16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

10(1/2x + 2) - 5 = 3(x - 6) + 1

Step 2: Solve for x

Distribute:                                   5x + 20 - 5 = 3x - 18 + 1Combine like terms:                   5x + 15 = 3x - 17Subtract 3x on both sides:         2x + 15 = -17Subtract 15 on both sides:         2x = -32Divide 2 on both sides:              x = -16

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                     10(1/2(-16) + 2) - 5 = 3(-16 - 6) + 1Multiply:                                10(-8 + 2) - 5 = 3(-16 - 6) + 1Add/Subtract:                       10(-6) - 5 = 3(-22) + 1Multiply:                                -60 - 5 = -66 + 1Subtract/Add:                       -65 = -65

Here we see that -65 does indeed equal -65.

∴ x = -16 is the solution of the equation.

The GCF of 15 and 27 is _____. Numerical Answers Expected! Answer for Blank 1:

Answers

Answer is 3, you can try it. I’m pretty sure it’s correct.

Answer:

the answer is 3 i just did the test and btw i like your profile pick anyways not the point just know the answer is 3

Step-by-step explanation:

passes through (6. -6), slope = 5

Answers

Answer:

well you need to rise/run. so rise 5 and over 1 to find your answer. repeat the process if needed

Step-by-step explanation:

Given
n, find the value of x.

I think the answer is 109 but I’m not sure

Answers

Answer:

x=35 hope it helps see ☜☆☞

Answer is 35 degrees

See attachment

Corresponding angles are on parallel lines with a transversal line

There are two pairs of corresponding angles and they are congruent (same)

A and B = 35
B and C = 35

C is a vertical angle to D and vertical angles are congruent (same) = 35

Shannon's rectangle countertop is 3 feet wide.it is 3 times as long as it is wide.Find the length and the area of Shannon’s countertop.

Answers

AnswerArea: 27 square feet Length: 9 Feet

Step-by-step explanation:

So, first we need to find the length.

If the length is 3 times the width, we need to multiply the width times 3 to get the lenght. So, 3*#=9/ So the lenght is 9

Now, we need to find the area.>

We need to multiply length times width, so-

9*3=27

Write
3√2 +6
√2-1
in the form a +b√√2, where a and b are integers.

Answers

Step-by-step explanation:

Solution

3(√2+2)

Alternative Form

≈ 10.24264

Please help me out!
Brainiest will be given to the most accurate answer

Answers

Answer:

g(x) = -3x

Step-by-step explanation:

g(x)=3x reflected about x - axis is g(x) = -3x. It's kind of hard to explain but that's the right answer i'm pretty sure

Find the missing number so that the equation has infinitely many solutions.
3(-x + 3) = -3x +?

Answers

Answer: 9

Step-by-step explanation: First, solve the left side. Using the distributive property, the left side would be -3x + 9. The right side is the same, but missing the 9. Adding the 9 will make the value of x not matter (essentially infinite solutions).

Starting at 300 feet away, a car drives towards you. IT then passes you by at a constant speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds is given by the equation d=|300-48t|. AT what times is the car 60 feet from you?

The car is 60 feet away from you after___seconds and after _____ seconds.

Explain what 48t represents in the given equation.

Answers

The car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.

The 48*t part means the number of feet that the car moves in t seconds

At what times is the car at 60ft from you?

We know that the absolute value equation that models the distance is:

d(t) = |300 - 48*t|

Then what we need to solve is d(t) = 60, this is:

d(t) = 60 = |300 - 48*t|

That absolute value equation can be represented in two forms:

300 - 48*t = 60

300 - 48*t = -60

Solving these two we get the two times at which the car is at 60ft from you.

-48*t = 60 - 300

t = (60 - 300)/(-48)  = 5

t = (-60 - 300)/(-48) = 7.5

So the car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.

The 48*t part means the number of feet that the car moves in t seconds.

If you want to learn more about absolute value equations:

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Put a ring around the number with the largest value. 113 0.3030 0.0330 3 10 33%

Answers

Answer:

Step-by-step explanation: big aye

solve by the matrix method , x+y/5 -1=y-x​

Answers

10x - 4y = 5 (if it requires shorten)

Step-by-step explanation:

x + y/5 - 1 = y - x

<=> (5x + y - 1.5)/5 = 5(y - x)/5

<=> 5x + y - 5 = 5y - 5x

<=> 5x + 5x + y - 5y = 5

<=> 10x - 4y = 5

Can someone help with this please?

Answers

Answer:

<4 = 81

Step-by-step explanation:

we know that all the interior angles of a triangle will equal 180

so <1 + <2 + <3 = 180

we know that <4 is the exterior angle to <3

the exterior angle is equal to the angles opposite to its interior

<3 is the interior angle to <4

<1 and <2 are the angles opposite to <3

so <4 = <1 + <2

<4 = 42 + 39

<4 = 81

I need help plss
Hola

Answers

The answer is 3 7/8 reduced because according to the order of operations we do the parenthesis first so we add -1/8 with 2/5 and then we will add the answer which was 11/40 then we add that to 3 3/5 and then we will get the answer 3 7/8 ( I reduced this so it would be in a nicer format.) have a nice day and god speed (:

Subtract
3-9 = ???????

Answers

Answer:

-6

Step-by-step explanation:

come on

3 ( k - 5 ) = - 16.

Answers

Answer:

k = -1/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(k−5)=−16

(3)(k)+(3)(−5)=−16(Distribute)

3k+−15=−16

3k−15=−16

Step 2: Add 15 to both sides.

3k−15+15=−16+15

3k=−1

Step 3: Divide both sides by 3.

3k /3 = −1 /3

k =  −1 /3

As labor costs, an electrician charges

$36.50 per hour for himself, and $27.50

for his assistant. What would be the

total labor cost for a job taking 6 1/2 hours?
giving brainliest

Answers

Answer:

h=416$

Step-by-step explanation:

36.50h+27.50h= 64

64x6 1/2=

416 $

Answer:

416

Step-by-step explanation:

36.50+27.50=64

64*6=384

and then add 32 for the half an hour

384+32=416

Find the value of x by filling the blanks in the provided statement-reason solutions

Answers

Answer:

no picture?

Step-by-step explanation:

Find the distance between 6 and -2 on a number line

Answers

Answer:

8

Step-by-step explanation:

The distance between 6 and -2 is 8

(draw a number line and from 6 to -2 is 8 steps)

Consider the circle centered at the origin and passing through the point (-8,0) give the equation of the circle

Answers

Answer:

Step-by-step explanation:

The equation of circle that passes through origin is given by

And the given circle passes through (-8,0).

Substituting -8 for x and 0 for y, we will get

Order from least to greatest
11. 357
2. 1.02
13. .80
4. .002
15. .05
16. .40

Answers

Answer:

0.002 , 0.05 , 0.40 , 0.80 , 1.02 , 2 , 4 , 11 , 13 , 15 , 16 , 357

Step-by-step explanation:

11 , 357 , 2 , 1.02 , 13 , .80 , 4, .002 , 15 , .05 , 16 , .40

Jim wants to save money to open a tutoring center. He buys an annuity with a quarterly payment of 56$ that pays 3.7 interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 9 years.

Answers

Answer:

$78.01

Step-by-step explanation:

solve the equation 56(1+.037÷4)^4×9

ends up being 56(1.00925)^36

56(1.3930133899)

=78.0087

The total value of the annuity in 9 years is: $78.00

We have the following information available from the question is:

He buys an annuity with a quarterly payment of $56 that pays 3.7 interest, compounded quarterly.

Payments will be made at the end of each quarter.

We have to find the total value of the annuity in 9 years.

Now, According to the question:

The total value of the annuity in 9 years :

The equation will be :

[tex]= > 56(1+ \frac{3.7}{4} )^4^(^9^)[/tex]

=>56(1.3930)

=$78.00

Learn more about Compound interest at:

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Triangle MRN is created when an equilateral triangle is folded in half. What is the value of x?

A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units

Answers

Answer:

C. 4√3 units

Step-by-step explanation:

Edge 2021

The value of x is 4.

Option B is the correct answer.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

From ΔRMN,

NM² = RN² + RM²

8² = y² + x²

64 = y² + x² ______(1)

And,

From ΔRNS,

RN² = RS² + SN²

y² = z² + 6²

y² = z² + 36 ______(2)

And,

From ΔRMS,

x² = z² + 2²

x² = z² + 4 _______(3)

From (1), (2), and (3).

x² = y² - 36 + 4

x² = 64 - x² - 36 + 4

2x² = 64 - 36 + 4

2x² = 68 - 36

2x² = 32

x² = 16

x = 4

Thus,

The value of x is 4.

Learn more about the Pythagorean theorem here:

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GIVING OUT BRAINLIEST!!! PLS HELP ASSAPPP!!!!
Which statement is correct when solving the expression 5y^2-3y^2?

Add the coefficients (5 + 3).


Subtract the exponents (2 – 2).


Add the exponents (2 + 2).


Subtract the coefficients (5 – 3).

Answers

Answer:

C. Add the exponents (2+2)

D. Subtract the coefficients. (5-3)

2y^4

I hope this helped! :))

D. Subtract the coefficients

( b/c you can’t add exponents unless they have the same base )
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