Luci Lulu opened a cookie store in the mall. She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship x = −2000 p + 4000 . Find the maximum revenue Luci can make selling cookies in one day. Find the price she should sell the cookies for to make the maximum revenue.

Answers

Answer 1

Answer:

The price to make maximum revenue is 1 and the maximum revenue is 2000.

Step-by-step explanation:

Consider the provided information.

Revenue is the product of the number of sales and the sales price.

Here, [tex]p[/tex] is the price of a cookie and the number of cookies sold is [tex]x =- 2000 p + 4000[/tex].

[tex]\text{Revenue}=p(-2000 p + 4000)[/tex]

[tex]\text{Revenue}=-2000 p^2 + 4000p[/tex]

The above equation is a quadratic equation and the graph of the above equation will be a downward parabola because the coefficient of [tex]p[/tex] is negative.

The vertex(axis of symmetry) of a downward parabola has the maximum point.

The axis of symmetry is  [tex]x=\frac{-b}{2a}[/tex]  for the quadratic equation [tex]ax^2+bx+c=0[/tex].

By compare Revenue equation with [tex]ax^2+bx+c=0[/tex], we get:

[tex]x=p, a=-2000, b=4000 \text{ and } c=0[/tex]

Now put the respective values in the formula [tex]x=\frac{-b}{2a}[/tex] .

[tex]p=\frac{-4000}{2(-2000)}[/tex]

[tex]p=1[/tex]

So revenue will be maximum for [tex]p=1[/tex].

Now put [tex]p=1[/tex] in [tex]\text{Revenue}=-2000 p^2 + 4000p[/tex]

[tex]\text{Revenue}=-2000 (1)^2 + 4000(1)[/tex]

[tex]\text{Revenue}=-2000 + 4000[/tex]

[tex]\text{Revenue}=2000[/tex]

Hence, the price to make maximum revenue is 1 and the maximum revenue is 2000.

Answer 2

Maximum revenue generated = $2000

Price at which the maximum revenue is generated = $1

Maximization of the revenue:

Steps to find the maximum revenue,

Find the equation for the revenue generated.Find the derivative of the expression for revenue and equate it to zero.Find the value of the variable and substitute it in the expression for the revenue generated.

Given in the question,

Price of one cookie = p    Linear relationship between the number of cookies sold 'x' and price of a cookie 'p',

        x = -2000p + 4000

Expression for the revenue generated = Price of one cookie × Number of cookies sold

R = p(-2000p + 4000)

R = -2000p² + 4000p

For the maximum revenue,

"Find the derivative of the expression for revenue and equate it to zero"

R' = -4000p + 4000 = 0

4000p = 4000

p = $1

For p = 1,

R = -2000(1) + 4000

R = $2000

       Therefore, for the price of one cookie as $1, maximum revenue generated will be $2000.

Learn more about the maximization here,

https://brainly.com/question/11859895?referrer=searchResults


Related Questions

What is 8/9 of 360 degree ?

Answers

Answer:

320 degrees.

Step-by-step explanation:

A parachute slows a skydiver from 85 m/s to 45 m/s in 4.5 seconds?

What is the acceleration of the parachute? A. 8.9 m/s2 B. -8.9 m/s2 C.0.1 m/s2 D. -0.1 m/s2​

Answers

Answer:

c - because if u divide u will get your answer sorry if im not makeing sense

Help me out i need help

Answers

Answer:

false, true and false

Step-by-step explanation:

PLEASE HURRY!!!!!!!
I PROMISE TO VOTE BRAINLIEST!!!!!!

Answers

it’s the last one. hjsksios
it is the last one ^^^^

Please help!!

Write the sum, and then write an equivalent expression by collecting like terms and removing parentheses

b. 2x - 7 and the opposite of 2x

Answers

Answer :

Sum = 2x-7 + (-2x) and equivalent expression = -7

Step-by-step explanation:

First number is (2x-7) and other number is opposite of 2x i.e. (-2x).

We need to write the sum of 2x - 7 and the opposite of 2x

Opposite of 2x is (-2x)

Sum means to add the number :

2x-7 + (-2x)

Removing parentheses,

2x-7 - 2x

Taking like terms together,

2x-2x-7= 0-7

= -7

Hence, the answer is -7.

Simplify. 4(w-5)-6w please help ASAP

Answers

Answer:

-2w-20

Step-by-step explanation:

distribute => 4w-20-6w = -2w-20

Answer:

-2w - 20

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Terms/Coefficients/Degrees

Step-by-step explanation:

Step 1: Define

4(w - 5) - 6w

Step 2: Simplify

Distribute 4:                    4w - 20 - 6wCombine like terms:       -2w - 20

For homework, a teacher instructs her students to choose a county in their state for a social
studies project. Since they live in a small state, repeats are allowed.
Are these two events dependent or independent?

Answers

Answer:

they are dependent

Step-by-step explanation:

I WILL GIVE YOU BRAINLY PLSS


What is the solution of x + 6 11
C. x –1

PLSS SHOW YOUR WORK PLSS

Answers

-1+6)11
6x11=66
-1+66= 65

65 is the answer

I need help I don’t get the question

Answers

They are equal to each other
9x - 7 = 7x - 3
2x = 4, x = 2
Solution: x = 2

Answer:

2

Step-by-step explanation:

9x-7 = 7x-3

9x-7x = 2x

2x -7 = -3

   +7   +7

2x=4

x=2

In Ms. Price's class, students were asked to name the sport that they watch most often on
television
8 students named baseball,
7 students named football,
5 students named basketball,
What is the ratio of the number of students who watched basketball most often to the total
number of students? *
11 point

Answers

Answer:

The ratio of number of students who watched basketball most often to the total number of students is 5 to 20 or 5:20

Step-by-step explanation:

Because 5 students named basketball as the spot the watch most often on television, while 8 of them said baseball and 7 said football. To find the total numbers of students we have to add all the students together so 8 + 7 is 15 and 15 + 5 is 20.

Hoped this help :)

A battery factory typically produces 12,000 batteries per day and uses 50 boxes for packing the battiest. If the number of boxes needed for packing is proportional to the number of batteries produced, how many more boxes would be needed in a day when 18,000 battiest are produced

Answers

Answer:

Number of extra boxes= 120

Step-by-step explanation:

Giving the following information:

Batteries per box= 50

Number of batteries= 18,000

Number of batteries in ecxess= 6,000

We need to calculate the number of boxes required to cover the 6,000 extra batteries:

Number of extra boxes= number of batteries / batteries per box

Number of extra boxes= 6,000 / 50

Number of extra boxes= 120

Simplify the expression.
0.2(2b - 15c)

Answers

Step-by-step explanation:

=0.2(2b-15c)

=0.4b-3c

hope it helps.


An orange cone has an
exact volume of 1207T ft3.
What is the height of the
cone if the radius is 6 ft?

Answers

Answer:

32.01 ft

Step-by-step explanation:

Step one:

given data

Volume of 1207T ft3.

the radius is 6 ft

Step two:

The volume of a cone is given as

[tex]V=1/3 \pi r^2h[/tex]

substitute

1207= 1/3*3.142*6^2*h

1207= 37.704h

divide both sides by 37.704

1207/37.704= h

h= 32.01 ft


Please help me. I need a step by step explanation.

Answers

Answer:

u can make me branliyest then i will help u

Step-by-step explanation:

Answer:

Answer for the first part: x = 0 so f(x) = 4

Answer for the second part: f(-2) = 2

Step-by-step explanation:

In order to solve the first prat of the problem you will just have to find a point on the function that has a y coridnate of 4, and the x cordinate of the exactly the same point will be the answer to your question. So in our case there is only one point like that and it (0,4). So that means the value of x for whcih f(x) = 4 is x = 0.

Now in order to answer the second part of this problem you will just have to find on a function with the x coridnate being -2, and the y cordinate of the exactly the same point will be the answer. In our case there is only one point liket aht and it is the point (-2,2). So that means taht the answer to the second part of the problem is f(-2) = 2.

Which does the ratio 17:44 represent?

Answers

Answer:

Step-by-step explanation:

the part-to-whole relationship between homework help and sports

Which value is not equivalent 0.37 0.370 37/100

Answers

0.370 is not equivalent
0.370 is equivalent to 370/1000 which is different than 37/100

6d + 7 = 61 what does d equal?

Answers

Answer:

i would reword this to 6x+7=61

Step-by-step explanation:

So.  

move the 7 to the right side of the equation but as an opposite number so in this case its gonna be a negative

61-7=54

then you divide the number and get your missing numbers

54/6=9

d=9

plug it in

6(9)+7=61

D is equivalent to 9

61 minus 7 is 54 what is 54 divided by 6?? 9 so the answer is 9

Can someone help me with this, I don't understand.​

Answers

3rd one is the answer

If you put 3 to the x, then the y is 5
Also another ones too

What is 37 / 492 show your work

Answers


The answer is this!! (Look in picture)

Rajan had 30 dollars to spend on 3 gifts. He spent 9 1 4 dollars on gift A and 5 4 5 dollars on gift B. How much money did he have left for gift C?

Answers

Answer:

$15 1/10

Step-by-step explanation:

Given that :

Total amount to spend = $30

Amount spent on Gift A = $9 1/4

Amount spent on Gift B = $5 4/5

Amount left to spend on gift C ;

$30 - (9 1/4 + 5 4/5)

$30 - (37/4 + 29/5)

$30 - (185 + 116)/20

$30 - 298/20

30/1 - 298/20

$(600 - 298) / 20

$302/20

$15 2/20

= $15 1/10

Please help *I’ll mark you as a brnlist please please ASAP ASAP please help me please

Answers

Answer:

12.6

Step-by-step explanation:

Given

with reference angle 57°

perpendicular (p) = y

hypotenuse (h) = 15

Now

sin 57° = p / h

0.84 = y / 15

y = 0.84 * 15

y = 12.6

Hope it will help :)


Solve for x
30°
9x - 3

Answers

180 = 90 + 30 + (9x - 3)
60 = 9x - 3
63 = 9x

x = 7

PLEASE HELP WILL MARK BRAINLIEST!!!!

Answers

No the line will be vertical on point one

Work out the value of (1.7X10^4) X (8.5X10^-2) in standard form

Answers

answer is 1.445 x 10^3

Answer:

1.445 × 10³ hope it helped goodluck!

A line has a slope of 6 and a y-intercept of 5. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

The equation in slope-intercept form is y = 6x + 5

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

m is the slopeb is the y-intercept

Let us solve the question

∵ A line has a slope of 6

∵ m is the slope of the line

m = 6

∵ The line has a y-intercept of 5

∵ b is the y-intercept

b = 5

→ Substitute the values of m and b in the slope-intercept form

∵ y = m x + b

∴ y = 6x + 5

The equation in slope-intercept form is y = 6x + 5

HELP IT NOT FORM IT FOR MY LITTLE SIS IM TO LAZY PLEASE HELP!!!!
1. 1/2 x 2/3
2.1/2 x 2/3 x3/4
3. 1/5 x 1/2 x 7/8
4. 1/8 x 4/7
5. 2/3 x 1/6
6. 2/5 x 1/4
7. 7/54 x 9/49
caculate
1. [tex](2/3)x^{2}[/tex])
2. [tex]1 1/2x^{2}[/tex]

Answers

1. 2/6
2. 1/4
3. 7/80
4. 4/15
5. 2/18
6. 2/20
7. 63/2,646

Pls help I will give BRAINLIEST ​

Answers

Answer: M<2=38 m<3=142 m<4=38

Step-by-step explanation:

142+142+38+38=360-Both side

142+38=180- one side

180-142=38

Answers:

angle 2 = 38 degreesangle 3 = 142 degreesangle 4 = 38 degrees

========================================================

Explanation:

Angle 1 is given to be 142 degrees. Angle 3 is equal to this measure since vertical angles are congruent. Vertical angles are angles that form when you have an X shape like this. They are opposite angles.

Angles 2 and 4 are the other pair of congruent vertical angles. This means angle 2 = angle 4.

Note how angle 1 and angle 2 form a straight line. These two angles add to 180.

(angle1) + (angle2) = 180

(142) + (angle2) = 180

angle2 = 180-142

angle2 = 38 degrees

angle 4 is also 38 degrees since angles 2 and 4 are a congruent vertical angle pairing.

HELP!!!!! Suppose the distance between two cities on a map is 5.2in the scale is 1 in =80miles what's the actual distance between the cities.

A) 408 miles
B) 400 miles
C) 424 miles
D) 416 miles

Answers

Answer:

80*5.2= 416

D: 416 miles

i need help fast with this problem

Answers

Answer:

6 is the answer

Step-by-step explanation:

please help>>>>>>>>>>>>>>>>

Answers

Answer:

The answer is B, -5 is a rational number and integer! :)

Step-by-step explanation:

Answer: My guess is integer only

Step-by-step explanation:

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