given the weekly demand curve of a local wine producer is p= 50-0.1q, and that the total cost function is c= 1500+ 10q, where q bottles are produced each day and sold at a price of $p per unit. a)Express the weekly profit as a function of price.b) at what price must a bottle of wine be sold to realise maximum profit. c) what is the maximum profit that ca be made by the producer

Answers

Answer 1

Answer:

a)the weekly profit as a function of price is[tex]P=-10 p^2 + 600 p - 6500[/tex]

b) a bottle of wine be sold at $30 to realise maximum profit

c) the maximum profit that can be made by the producer is $2500

Step-by-step explanation:

The weekly demand curve of a local wine producer is p= 50-0.1q

p = price

q = quantity

Revenue function R =Price \times Quantity

R=(50-0.1q)q

[tex]R=50q-0.1q^2[/tex]

Cost function: c= 1500+ 10q

Profit function=R(x)-C(x)

Profit function= [tex]50q-0.1q^2-1500-10q[/tex]

Profit function= [tex]40q-0.1q^2-1500[/tex]   ----1

We have q = 500 - 10 p using p = 50 − 0.1q

[tex]P=-0.1 (500 - 10 p)^2 + 40 (500 - 10 p)- 1500\\P= -10 p^2 + 600 p - 6500[/tex]

General quadratic equation:[tex]ax^2+bx+c=0[/tex]

On comparing

a = -0.1 , b = 40 , c = -1500

Maximum Profit is at q = [tex]\frac{-b}{2a}=\frac{-40}{2(-0.1)}=200[/tex]

To find price must a bottle of wine be sold to realise maximum profit

p= 50-0.1q

p= 50-0.1(200)=30

Substitute the value of q in profit function(1) get the maximum profit

So, Profit function= [tex]40\left(200\right)-0.1\left(200\right)^{2}-1500=2500[/tex]

Hence

a)the weekly profit as a function of price is[tex]P=-10 p^2 + 600 p - 6500[/tex]

b) a bottle of wine be sold at $30 to realise maximum profit

c) the maximum profit that can be made by the producer is $2500


Related Questions

An 8-question true or false quiz is given to a class. If Lee guessed every question,
how many would she expect to be correct?

Answers

Answer:  4

Work Shown:

n = number of questions = 8

p = probability of getting a question correct = 1/2 = 0.5

n*p = number of questions we expect Lee to get correct

n*p = 8*0.5

n*p = 4

We expect Lee gets about 4 questions correct.

4 question that lee guessed would be correct.

There  8 question of true and false.
Lee guessed every question.

What is probability?

Probability can be defined as ratio of favorable outcomes to the sample of events.

Here,
Probability of guessing right answer = 1/2 = 0.5
Probability of lee guessing right answer out of 8 question.
= 0.5 x 8
= 4

Thus, 4 question that lee guessed would be correct.


Learn more about probability here:
https://brainly.com/question/11234923

#SPJ2

Five less than three times a number is 1. Find the number

Answers

Answer:

n = 2

Step-by-step explanation:

Step 1: Write equation

"Five less" = subtract 5

"three times a number" = 3 × n, or 3n

"is 1" means = 1

3n - 5 = 1

Step 2: Solve for n

Add 5 to both sides: 3n = 6Divide both sides by 3: n = 2

Fill in the missing terms.

a) 1 : 2 = ___ : 4 b) 1 : ___ = 3 : 6 c) 3 : 5 = ___ : 10

d) 1 : 5 = 3 : ___ e) ___ : 6 = 1 : 3 f) 9 : 15 = ___ : 5

Answers

a) 2

b) 2

c) 6

d) 15

e) 2

f) 3

Evaluate the expression. |18 – 4| 22 14 –14 –22

Answers

Answer:  B) 14

Work Shown:

|18-4|

|14|

14

You subtract 18-4 to get 14. Applying absolute value on a positive number leads to the same result.

Answer:

14

Step-by-step explanation:

|18 – 4|

First find the value inside the absolute value bars

18-4 is 14

|14|

Then take the non negative value

14

If an object is projected upward from ground level with an initial velocity of 48ft per​ sec, then its height in feet after t seconds is given by ​s(t)= -16t^2+48t. Find the number of seconds it will take to reach its maximum height. What is this maximum​ height? The object will take __ ​second(s) to reach its maximum height. (Simplify your​ answer.) The maximum height reached by the object is __ feet. (Simplify your​ answer.)

Answers

Answer:

t = 1.5 s and s(t) = 36 feet

Step-by-step explanation:

The height reached by an object as a function of time t is given by :

[tex]s(t)= -16t^2+48t[/tex] ...(1)

t is in seconds

To find the maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]

[tex]\dfrac{d( -16t^2+48t)}{dt}=0\\\\-32t+48=0\\\\t=\dfrac{48}{32}\\\\t=1.5\ s[/tex]

It will take 1.5 seconds to reach its maximum height.

Put t = 1.5 s in equation (1), such that,

[tex]s(1.5)= -16(1.5)^2+48(1.5)\\\\s(t)=36\ \text{feet}[/tex]

The maximum height reached by the object is 36 feet.

the area of the larger square is ____ times larger than the area of the small square

Answers

Answer:

The area of the larger square is 16 times larger than the area of the small square.

the percentage of boys in a school is 60%, and the number of girls are 200, calculate the number of boys and the total number of students?


Answers

Answer:

Boys: 300 or 60%, girls: 200 or 40%, total number of students: 500 or %100

Step-by-step explanation:

So basically:

1. We know that 60% is boys and we're trying to figure out the exact amount. We know the other 40% (girls) is a total of 200.

2. First take the 40% and half it so we get 20% in order to do that we have to do the same to the 200 girls and half the number into 100. Now we know 20% is equal to 100 students. Given that information we would multiply the 20% by 3 to get the 60% of boys. Now we would also multiply the 100 by 3 and now we have 300.

3. We now know that we have 300 boys and 200 girls. Add them together for the total of students and you get 500.

I hope this helps:)

500
100% - 60% is 200 people
So 40% is 200 people
20% is 100 people and so 100% (full amount) would be 100 x 5 (how do you get from 20 to 100, you multiple by 5 so you do the same to the 100).
Gives you a total of 500

What is 7/9 divided by 1/3???????

Answers

Answer:

0.259...

Step-by-step explanation:

(2a-b-c)³+(2b-c-a)³+(2c-a-b)³ factorise​

Answers

Answer:

Sowy but try Mathwa y

Step-by-step explanation:

What is the equation of a quadratic function that has zeros -6 and -2?

Answers

Answer:

[tex]y=x^{2} +8x+12[/tex]  is the quadratic function.

Step-by-step explanation:

We know that -6 and -2 are the zeros. So, they are both equal to x.

x = -6 and x = -2

Add them to x.

(x + 6) (x + 2)

Now, multiply the two binomials together.

[tex]x^{2} +6x+8x+12[/tex]

Combine like terms.

[tex]y=x^{2} +8x+12[/tex]

[tex]y=x^{2} +8x+12[/tex] is the answer.

This question is hard and I don’t know it may u please help

Answers

Answer:

Mark's total salary is 22,260

Step-by-step explanation:

well, his base salary is 21,000.

if you look at the diagram, the added bonus is 6% of the base salary.

6% can be rewritten as 0.06

0.06 * 21,000 = 1,260

the total salary is just the base salary and the bonus salary added together.

21,000 + 1,260 = 22,260

How do I plot the coordinates (2,-4)

Answers

you need a graph , so the 2 would go on the x axis, the one going sideways, the -4 goes on the y axis, the up and down line, it should be below the x-axis

Answer:

the first number is the x axis and the second is the y axis so first find the x axis and plot the first number on there then do the same to the y.

Step-by-step explanation:

What do solving absolute value equations and solving quadratic equations have in common?

Answers

Answer:

They often have more than one solution.

Answer:

Step-by-step explanation:

Quadratic equations are equations that when rearranged using the 5 operations can yield a polynomial of degree 2 on one side of the equation and 0 on the other. There are 3 commonly taught methods for solving quadratic equations. These methods are factoring, completing the square, and the quadratic formula. These functions are most commonly used to model projectiles, disregarding air resistance.

When using the factoring method one attempts to write a degree 2 polynomial as the product of two degree 1 polynomials. This method works because if we multiply two degree one polynomials together we find  

For example: When factoring , we want to find two number a, b whose product is 6 and sum to 5. The values of a and b we are looking for are 2 and 3.

The method of completing the square centers around using the five operations to replace the original equation with an equivalent equation of the form  by taking advantage of the fact that

The absolute value function takes the value of a number, regardless of whether it is positive or negative. Some problems that the absolute value is useful for modeling include an object bouncing on the ground.

For example, , since we do not care about the negative sign.

Example: Solve  

Solution: Since the absolute value does not care about whether a number is positive or negative, if  then  or . Then we can solve each equation individually to find that x = 1 or 5.

Using the distributive property, an expression equivalent to 34 + 16 is
A.2(17+ 8)
B.17(2+8)
C. 34+ (4) (4)
D. (2)(17) + (4) (4)​

Answers

Answer:

A. 2(17+8)

Step-by-step explanation:

distribute and you get 2x17=34 and 2x8=16

Car A travels 127 miles in 4 hours. Car B travels 350 miles in 4 hours. Car C travels 583 miles in 14 hours. Which car has the fastest average speed?

Answers

B but look at the image to understand y

Answer:

B is the answer

what number can be added to 55 and have 45 and 9 as thier greatest common factor?

Answers

Answer:

36

Step-by-step explanation:

Which relation is a function?

Answers

Answer:

D

Step-by-step explanation:

To find out whether a graph is a function or not, you can use the vertical line test, which means if you were to draw a vertical line on the graph at any point,  if it would cross over 2 lines, it's not a function. D is the only graph that wouldn't fail the vertical line test.

Which of the following is equal to 5/7-4/7 (a) 0 (b) 1 (c) undefined (d) 1/7

Answers

Answer:

It's 0.142857

Step-by-step explanation:

Answer:

your answer is d.1/7

Step-by-step explanation:

all you have to do is subtract 5-4 which is 1 then add 7 as the denominator

Which ordered pair is the solution to the system of linear equations Negative 5 x + y = 26 and 2 x minus 7 y = 16?

Answers

9514 1404 393

Answer:

  (-6, -4)

Step-by-step explanation:

If you're going to use technology to answer your questions, you may as well use appropriate technology: a graphing calculator. It shows the solution to the system is the ordered pair (-6, -4).

__

The first of the given equations can be solved for y, then that used to substitute for y in the second equation.

  y = 5x +26

  2x -7(5x +26) = 16

  2x -35x -182 = 16

  -198 = 33x . . . . . . . . add 33x-16

  -6 = x . . . . . . . . . . . . divide by 33

  y = 5(-6) +26 = -4 . . . find y

The solution is (x, y) = (-6, -4).

Line $1$ represents the graph of $3x + 4y = -14$. Line $2$ passes through the point $(-5,7)$, and is perpendicular to line $1$. If line $2$ represents the graph of $y=mx +b$, then find $m+b$.

Answers

Answer:

15

Step-by-step explanation:

First, solve for Line 1

3x + 4y = -14

move the x to the right of the equation

4y = -3x - 14

divide the whole equation by 4

y = -3/4x - 14/4

Line 1 is y = -3/4x - 7/2

Then, solve for Line 2

Since Line 2 is perpendicular, change the sign of the slope of Line 1 and then get the reciprocal of that.

-3/4 to 3/4 to 4/3

4/3 is the slope of Line 2.

Now, we want to find what the b of the equation is, so we can plug in our x (-5) and our y (7) into the y=mx+b equation to find b. The 4/3 is the m or the slope.

y = mx + b

plug in the y, m, and x into the equation

7 = (4/3)(-5) + b

multiply the m and x together

7 = -20/3 + b

add 20/3 to both sides so it will cancel out on the right of the equation and be added to the 7 on the left of the equation

41/3 = b

So, m = 4/3 and b = 41/3

Add them together and you get 45/3 or 15.

I hope this helped!

At the zoo, the ratio of elephants to hippos is 1.2. So for every elephant, there
are hippos

Answers

Answer:

2 hippos

Step-by-step explanation:

Answer:

For every elephant, there are 2 hippos.

Solve the following equations.
1) 10 + x = 13

2) y - 13 =23


3) 4b = 24

4) m/5=7

Answers

Answer:

1) x = 3

2) y = 36

3) b = 6

4) m = 35

Step-by-step explanation:

1) x = 13-10 =3

2) y = 23+13 =36

3) b = 24÷4 =6

4) m = 5×7 =35

can medicine cure depression if you have it because of someone you’ve loved for 2 years but they just don’t care about you..? i’ve tried for 2 years to get over them and till this day i’m still ✨crying✨ every night :/ i need help i need answers to why this is happening.. i’m sorry for being depressed but i just can’t stop how much i love them.. and i pray for god but he never answers he just puts more pain in my life.. love you all and thank you for reading this if you did your all amazing..

Answers

Answer:

there is mutable ways to cure depression rather it would be therapy or antidepressants if you need help find a therapist or cirotherapist that can solve your pain and can prescribe medication

The following graph shows a proportional relationship

Answers

Answer:

for every 5 units to the right, there is 1 unit up

the slope is y = 1/5

the registration fee for a used car is 0.8% of the sale price of 5,700. How much is the fee

Answers

Answer:

1,140

Step-by-step explanation:

subtract the percentage from the total

4 equal piece of rope out of 2 1/2 inch how long is each piece​

Answers

Answer:

1/4 inches

Step-by-step explanation:

To get 4 equal pieces you need to cut the 2 equal pieces in half, which half of 1/2 inches is 1/4 inches.

A rectangle has a perimeter of 80. if the length is four more than twice the width, what is the length of the rectangle ​

Answers

Answer:

28

Step-by-step explanation:

l = length

w = width

p = perimeter

w = w

l + l + w + w = p (adding all the rectangle's sides together gets us our perimeter)

l = 2w + 4 (four more than twice the width)

Substitute 2w + 4 for 'l' in the original equation

(2w + 4) + (2w + 4) + w + w = 80

Solve equation normally:

6w + 8 = 80

6w = 72

w = 72/6 = 12

(w = 12)

Length = 2w + 4

Substitute 12 for 'w':

2(12) + 4 = l

24 + 4 = l

28 = l

The length is 28

Morgan can type 18 words
per minute. How long will it
take her to type 3
paragraphs? (Each
paragraph has 30 words)

Answers

Answer: it will take 5 minutes.

It will take 5 minutes

Ryan and his brother are at a carnival. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will each meet back at the ferris wheel from time to time to see whether the other is ready to leave. Ryan checks the ferris wheel every 15 minutes. His brother checks in every 24 minutes. At what time will they meet at the ferris wheel again. (Hint: Don't forget you're looking for a time)

Answers

Answer:

3:00pm

Step-by-step explanation:

The idea hear is to find the least common multiples of 15 and 24

Given that they separated at exactly 1:00pm

the multiples are

15= 15,30,45,60,75,90,105,120

24= 24, 48,72,96,120

the multiples common is 120

Therefore they will meet in 120minute, which is 2 hours time \

hence the time will be 3:00pm

An atom is neutral. Its nucleus contains two protons and two neutrons. How
many electrons does the atom have?

Answers

Answer:

2 electrons

Step-by-step explanation:

An atom is neutral if it has no charge. That means the positive and negative charge balance each other out.

There are two protons, so that is a charge of +2. To make the charge 0, there needs to be a charge of -2. -2= 2 electrons.

Answer:

Answer is 2

Step-by-step explanation:

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