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:

Step-by-step explanation:

From the given information:

a) To express the weekly profit as a function of price

Cost =C(q) = 1500 + 10q

Revenue = p×q = (50 − 0.1q)×q = 50q - 0.1q²

Revenue = 50q - 0.1q²

Weekly profit = Revenue - Cost

P(q) = (50q -0.1q²) - (1500 + 10q)

P(q)= -0.1 q² + 40 q - 1500  

However, q = 500 - 10 p using p = 50 − 0.1q

P= -0.1 (500 - 10 p)² + 40 (500 - 10 p) - 1500

P= -10 p² + 600 p - 6500

b)

The price at which the bottle of the wine must be sold to realise a maximum profit can be determined by finding the derivative and then set it to 0  

P' = 0

= -20p+600 = 0

20p = 600

p = 600/20

p = $30

c)

The maximum profit that can be made by the producer is:

P= -10(30)² + 600(30) - 6500

P = - 9000 + 18000 - 6500

P = $2500


Related Questions

Water is poured into a container at a steady rate. After six minutes, 9.6 gallons of water are in the container. Let g represent the number of gallons of water in the
container after t minutes.
Select the equation that represents the relationship between g and t.
g= 0.6254
gt = 0.625
1.6g =1
g = 1.6t

Answers

Answer:

g = 1.6t

Step-by-step explanation:

Here, we want to select the equation that shows the correct relationship between g and t

We are told that after 6 seconds, we have 9.6 gallons of water

So the amount per second will be 9.6/6 = 1.6 gallons per second

So the relationship between the two will be

g = 1.6t

Where t is the time and g is the gallons

What is the result of solving this equation for x?

y−b=m(x−a)

Answers

Answer:

( y-b) / m    +a = x

Step-by-step explanation:

y−b=m(x−a)

Divide each side by m

(y−b)m=m/m(x−a)

( y-b)/m  = x-a

Add a to each side

( y-b) / m +a = x-a+a

( y-b) / m    +a = x

Answer:

y − b = m(x − a)

y − b = mx - ma

(y - b) / m = x - a

((y-b)/m) + a = x

a function can be classified as one-to-one correspondence, one-to-many correspondence and many-to-one correspondence.​

Answers

For a one-to-one mapping, all the elements of the domain R must have a unique element in the co-domain R

For a one-to-many mapping, an element of the domain R must have more than one element in the co-domain R

For a many-to-many mapping, all elements of the domain R must have a unique element in the co-domain R

Mappings can be classified as one-to-one, one-to-many, and many-to-one

A mapping of a set of domain R to another set of domain X is expressed as:

f: X→ R where:

X is the domain

R is the co-domain

For a one-to-one mapping, all the elements of the domain R must have a unique element in the co-domain R

For a one-to-many mapping, an element of the domain R must have more than one element in the co-domain R

For a many-to-many mapping, all elements of the domain R must have a unique element in the co-domain R

Learn more here: https://brainly.com/question/24138383

I need help finding the slope, the Y intercept and the equation for this graph???

Answers

Answer:

Step-by-step explanation:

y intercept is 4

slope is 6/3 is 2

y=2x+4

12a^3b^2c
A: The degree is 6
B: The degree is 3
C: The degree is 4
D: The degree is 5

Answers

Answer:

b. the degree is 3

Step-by-step explanation:

degree is the highest exponent

5. a. After receiving a 3 % raise, Randy's salary is now $4 120. What was her
original salary? Her original salary was $

Answers

Answer:

$4000.

Step-by-step explanation:

Let x = original salary

x * 1.03 = $4,120.

x = 4000

need help with 6 easy math problems​

Answers

Answer:

image not clear.

so I can't answer it .

Answer:

Step-by-step explanation:

10v - 6 = 24

10v = 24 + 6

10v = 30

v = 30/10 = 3

7 = 6r - 17

7 + 17 = 6r

24 = 6r

24/6 = r

4 = r


1. The length of a rectangular parking lot is 8m longer than its width. The area of
the parking lot is 560m2. What is the length of the parking lot? How about its
width?​

Answers

Answer:

Length = 20

Breadth = 12

Step-by-step explanation:

I don't know the answer ​

Answers

f(8)= (8)^2 + 4(8)

=(64) + (32)

=96

Hope this helps!

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.

What is the equation of the line that passes through the point (-4, 2) and has a
slope of 1/4?

Answers

Answer: The equation of the line is y=1/4x + 3

Step-by-step explanation:

To get the equation, you have to set it up:

y=1/4x + b

Plug in the coordinates (-4, 2) next:

2=1/4(-4) + b

Solve:

2= -1 + b

add one on both sides:

3= b

Use the information to get the equation:

y=1/4x + 3

I hope this helps!!

Answer:

dfjhbgvdsasdfgf

Step-by-step explanation:

Solve for x: 3 < x +3 < 6

Answers

Answer: 0< x < 3

Step-by-step explanation:

Hope this helps!

What is the surface area?
4 ft
10 ft
5 ft
square feet

Answers

200 square feet. I think. Hope I’m right.

A grocery store sells a bag of 6 oranges for $4.20. If Ayden spent $2.80 on oranges, how many did he buy?

Answers

Answer:

4 oranges.

Step-by-step explanation:

First, you find the unit rate of cost per orange, which is $0.70, then divide that by $2.80.

The table shows ticket prices for the local minor
league baseball team for fan club members and
non-members. For how many tickets is the cost the
same for club members and non-members?

Answers

Answer:

2x club member ticket = 1x non-club member ticket

Suppose m <6= 147º. Find <1 and m<3

Answers

Answer:

∠ 1 = ∠ 3 = 33°

Step-by-step explanation:

∠ 3 and ∠ 6 are same- side interior angles and are supplementary , thus

∠ 3 + ∠ 6 = 180° , that is

∠ 3 + 147° = 180° ( subtract 147° from both sides )

∠ 3 = 33°

∠ 1 and ∠ 3 are vertical angles and congruent, thus

∠ 1 = ∠ 3 = 33°

look at image and answer plz

Answers

Answer:

y=64 :)

Step-by-step explanation:

40/ [tex]\frac{5}{8\\}[/tex]= 64

pls give brainliest if correcto

5/8 z + (-2.5) = 2.5 worded

Answers

Answer:

Step-by-step explanation:

2.5 subtracted from (5/8)th of z gives 2.5

y= -5/6x + 4 in slope intercept form?

Answers

Answer:

DOMAIN:

solution: x<0 or x>0

interval notation: ( -∞,0)U(0,∞)

RANGE:

solution :f(x) < 4 or f(x) >4

interval notation: (-∞,4)U(4,∞)

X-INTERCEPTS:

(5/24,0)

ASYMPTOTES:

vertical: x=0

horizontal: y=4

EXTREME POINTS:

none

Step-by-step explanation:

lol i didnt knw how much info u needed i hope this helps

The slope intercept form is y=mx+c, So y= -5/6x + 4 is in slope intercept form.

What is general equation of slope intercept form?

The general equation of slope intercept form is y=mx+c

where m is the slope and c is the y intercept

The given equation is y= -5/6x + 4, we have to check whether the given equation in slope intercept  form or not.

The given equation is y= -5/6x + 4...(1)

We know that general equation of slope intercept form is y=mx+c...(2)

As we compare equations (1) and (2), we find that equation (1) in the form of (2). so y= -5/6x + 4 is in slope intercept form.

Therefore y= -5/6x + 4 is in slope intercept form.

To learn more about slope intercept form click here : https://brainly.com/question/9682526

#SPJ2

What the heck is this?

Answers

Answer:

(2,-1)

Step-by-step explanation:

(-2+6)/2 (2+4)/2

5 (x +2)= 11 can someone please tell me what X equals with an explanation i judt dont get math i thought i did but i dont

Answers

X=1/5
Pls mark brainliest

Answer:

x = .1

Step-by-step explanation:

Multiply 5 times x and 5 times 2

You end up with this: 10x + 10 = 11

Then, subtract 10 on each side so you would get 10x = 1

Finally, divide 10 into 1 to get your answer of x = .1

Trent is drawing a diagram of his house for a school project. He decides that every 5 feet in real life should be 2 inches in the diagram. Trent's living room is 15 feet long. How long should Trent's living room be in his diagram?

Answers

Answer:

5 feet (60 inches) proportional to 2 inches is a 30:1 relationship.

15 feet (180 inches) in real life should equal 6 inches on the diagram.

180 divided by 30 = 6

Step-by-step explanation:

Answer:

6 inches

Step-by-step explanation:

-10 |h+5| -3= -83
what is the answer to this the topic is absolute value.

Answers

Answer:

the absolute value is 3,-13

What is the slope of the line that goes through the points (1,-2) and (3,6)?

A.) -4


B.) 2


C.) 4


D.) 1

Answers

Answer:

(C).  4

Step-by-step explanation:

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(1,\:-2\right),\:\\\left(x_2,\:y_2\right)=\left(3,\:6\right)\\\\m=\frac{6-\left(-2\right)}{3-1}\\\\m = \frac{6+2}{3-1}\\ \\m = \frac{8}{2} \\\\Simplify\\\\Slope = m = 4[/tex]

A package of 4 pairs of insulated socks costs ​$35.56 What is the unit price of the pairs of socks​?

Answers

8.89

:

Step-by-step explanation:

Answer: $8.89

Step-by-step explanation:

$35.56/4 = $8.89

1+1+2+3+4+5+6+7+8+9=?

Answers

Answer:

The answer is 46

Step-by-step explanation:

Self explanatory i just added them together

hope i helped :D

Reduce the fraction to lowest terms. x^3-x^2/x^4

Answers

Answer:

x^3-x^2

_______ =  x - 1 / x^2  (simplified by x^2)

x^4 ...?

Which of the following graphs represent a function? 4 graphs. Graph A is a curved line, graph b is horizontal, vertical, and then horizontal, graph C is a line with positive slope, graph D is a circle. a. Graph A and Graph C b. Graph A c. Graph D d. Graph B and Graph D Please select the best answer from the choices provided A B C D

Answers

Answer:

graph A

Step-by-step explanation:

Answer:

Graph A and graph C

Step-by-step explanation:im a real one omm

simplifying radicals pt.1 please help ASAP and explain if possible

Answers

The answer is c 20√2

What are the Slope and Equation of the graph?

Answers

Answer:

Slope=2

Equation of the Graph is y=2x-6

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