A company has determined that its profit for a product can be described by a linear function.
The profit from the production and sale of 150 units is $455, and the profit from
250 units is $895.
(i) What is the average rate of change of the profit for this product when
between 150 and 250 units are sold?
(ii) Write the equation of the profit function for this product.
(iii) How many units give break-even for this product?
(b) You are the CEO for a lightweight compasses manufacturer. The demand
function for the lightweight compasses is given by p = 40 − 4q
2where q
is the number of lightweight compasses produced in millions.It costs the company $15
to make a lightweight compass.
(i) Write an equation giving profit as a function of the number of lightweight compasses
produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit
of $18,000,000, but you would like to reduce production. What smaller number of
lightweight compasses could the company produce to yield the same profit?

Answers

Answer 1

Step-by-step explanation:

(a)(i) The average rate of change is:

(895 − 455) / (250 − 150)

4.4

(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change.  Using point-slope form:

y − 455 = 4.4 (x − 150)

Simplifying to slope-intercept form:

y − 455 = 4.4x − 660

y = 4.4x − 205

(a)(iii) The break-even point is when the profit is 0.

0 = 4.4x − 205

4.4x = 205

x = 46.6

(b)(i) The "demand function" is the selling pice of the compasses:

p = 40 − 4q²

where p is the price in dollars and q is the quantity in millions of units.

Profit is revenue minus cost.

P = R − C

P = pq − 15q

P = (p − 15) q

P = (25 − 4q²) q

P = 25q − 4q³

where P is the profit in millions of dollars and q is the quantity in millions of units.

(b)(ii) Find values of q when P = 18.

18 = 25q − 4q³

4q³ − 25q + 18 = 0

We know that q=2 is a root of this equation.  Using grouping:

4q³ − 8q² + 8q² − 25q + 18 = 0

4q² (q − 2) + (q − 2) (8q − 9) = 0

(q − 2) (4q² + 8q − 9) = 0

4q² + 8q − 9 = 0

Solve with quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)

q = (-8 ± √208) / 8

q = (-8 ± 4√13) / 8

q = (-2 ± √13) / 2

Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.


Related Questions

Which set of ordered pairs does not represent a function?

Group of answer choices

{(6, 0), (-9, 5), (1, -5), (0, 0)}

{(4, 6), (6, 8), (3, 2), (-6, 8)}

{(-9, -7), (-8, -7), (8, 2), (9, -5)}

{(-8, 6), (-8, 5), (-9, 4), (-5, 3)}

Answers

Answer:

the last one

Step-by-step explanation:

No points on a function can have the same x value, can you give me brainliest

what is a point-slope equation of the line with slope -10 that goes through the point (1,4)

Answers

Answer:

The answer is

[tex]y - 4 = - 10(x - 1)[/tex]

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

So we have the final answer as

[tex]y - 4 = - 10(x - 1)[/tex]

Hope this helps you

A parachutists speed during a free fall reaches 153 miles per hour. What is this speed in feet per second? at this speed, how many feet will the parachutist fall during 15 seconds of free fall? in your computations, use the fact that 1 mile is equal to 5280 feet. do not round your answer

Answers

153 miles x 5280 feet per mile = 807,840 feet per hour.

1 hour = 3600 seconds.

The speed is 807,840 feet / 3600 = 224.4 feet per second.

Distance in 15 seconds = 224.4 x 15 = 3,366 feet.

The height of the rocket after t seconds is given by the equation h(t) = -16t² + 42t

What is an equation?

An equation is an expression that shows the relationship between two or more variables and number.

1 mile = 5280 feet, 1 hour = 3600 seconds

153 miles per hour = (153 * 5280) / (3600) ft/s = 224.4 ft/s

After 15 seconds, height = 224.4 ft/s * 15 s = 3366 ft

The speed of the parachute is 224.4 ft/s, while after 15 seconds the distance fell was 3366 ft.

Find out more on equation at: https://brainly.com/question/2972832

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What sets of numbers are included in the real numbers

Answers

Answer:

−3, −2, −1, 0, 1, 2, 3

Pass necessary journal entries in the books of Narender for the month of March 2006

Answers

Please explain this question as I can't 'Pass necessary journal entries in the books of Narender for the month of March 2006'

On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C has points (negative 4, 3), (4, 4), and (1, 1). A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the image △A'B'C'? Check all that apply.
AB is parallel to A'B'.
DO,1/2(x, y) = (one-half x, one-half y)
The distance from A' to the origin is half the distance from A to the origin.
The vertices of the image are farther from the origin than those of the pre-image.
A'B' is greater than AB.

Answers

Answer:

A, B, C

Step-by-step explanation:

It's correct, I took the activity before the quiz and got it right.

Happy to help :3

PLEASE HELP!!! The sum of 2 consecutive itegers is 294. Write an equation for the integers.

Answers

Answer:

147

Step-by-step explanation:

Divide 294 by 2

a group a friends share 3 1/2 slices of cake. each friend get half a slice of cake. how many friends shared the slices of cake.

Answers

Answer:

7

Step-by-step explanation:

3×2

6+1

7

You multiple it by 2 since it is 1/2 and not a whole piece

Answer:

7

Step-by-step explanation:

3 1/2 divided by 2 is 7

Jake, Utah, renting with a friend
Hourly rate: $8.75/hour
Hours worked: 40/40
Commission rate: 2.75%
Sales amount: $7500
Expenses: everything.
Y
CO20

Answers

Answer:

What is the question?

Step-by-step explanation:

I will change my  answer if you put a clear question up...

13-4x=1-x Please help 20 POINTS

Answers

Answer:

x will equal to 4

x = 4

13-4x=1-x
+x = -13
3x = 12

Which number is closest to V6 ?

Answers

Answer:

2.44949

Step-by-step explanation:

hope this helps

Answer:

2.9

Step-by-step explanation:

Nina earned $35 babysitting. She went to the store and bought 2 CD's. The first CD she chose was priced at $13. The second CD was originally priced at $20.00 and was on sale for $15. After buying the CD's Nina then went to the grocery store with her mother. Her mother spent $6 on Nina's favorite brand of juice. How much money does Nina have left?

Answers

1 dollar

Explanation
15+13=28
28+6=34
35-34=1

IM GONNA FAIL OMG HELP ME ILL GOVE YOU POINTS!!

Answers

Answer:

Step-by-step explanation:

1. yes

2. no

3. -10 and 5

4. -6

5. 3x+3

6. 3x+4

7. 14xy^2-3y+7

8. -3y-7x

9. 10x -5

Answer:

1) yes they are if y is alone its just 1y so yes their like terms.

2)no 5xy^2 is different bc the exponent

3)5x-5

4)-6

5)3x+3

6)4+4x

7)14xy^2-3y+7

8)3y-7x

9)10x-5

Step-by-step explanation:

Let xy=6 and x2 + y2 = 23 what is the value of (x+y)??

Answers

Answer:

I'll assume that x2 = x^2 and y2 = y^2 and the answer is sqrt{35}.

Step-by-step explanation:

This problem invovles completing the square, so if I square (x+y), I get

x^2+2xy+y^2, and since xy = 6, 2xy = 12, 23+12 = 35, and your answer is sqrt{35}.

The late fee at the library is based on the number of days a book is late. Carter paid $1.08 for a book that was 9 days late. If his sister Sydney had a fee of $1.92 for a late book, how many days late was the book?​

Answers

Answer:

16 days

Step-by-step explanation:

1.08 $:9 days

1.92 $: x

1.08 x: 17.28

x = 16

0.5f - 2.3g

F= 12, g = 2

Answers

Hi there & welcome to brainly !

Answer:

[tex] \huge{ \bold{ \boxed{ \tt{1.4}}}}[/tex]

Step-by-step explanation:

[tex] \text{Given : f \: = \: 12 \: g = 2}[/tex]

[tex] \text{To \: find : Value \: of \: given \: expression}[/tex]

[tex] \text{Let's \: start}[/tex] :

[tex] \text{0.5f \: - 2.3g}[/tex]

Here, The values of f and g are 12 and 2 respectively. Plug the given values :

↦ [tex] \text{0.5 ∗ \: 12 - 2.3 ∗ 2}[/tex]

Multiply : 0.5 and 12

↦ [tex] \text{6 - 2.3 \: ∗ \: 2}[/tex]

Multiply : 2.3 and 2

↦ [tex] \text{6 - 4.6}[/tex]

Subtract 4.6 from 6

↦ [tex] \text{ \boxed{1.4}}[/tex]

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

The solution of the given expression will be; 1.4

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that  0.5f - 2.3g where f = 12 and g = 2

Now substitute 12 in for f and 2 in for g and solve;

0.5(12)  -2.3(2)

6 - 4.6

=1.4

To know more about an expression follow;

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The complete question is;

Evaluate the expression: 0.5f - 2.3g where f = 12 and g = 2

Rewrite the following equation in slope-intercept form.
17x + 18y = -6

Answers

Answer:

y= -17/18x-1/3

Step-by-step explanation:

The slope-intercept form of the equation is y = (-17/18)x -1/3.

What is linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A linear equation 17x + 18y = -6.

To find the slope-intercept form:

Simplifying,

17x + 18y = -6

18y = -6 -17x

y = -17/18x -1/3

Therefore, y = (-17/18)x -1/3 is the slope-intercept form.

To learn more about the linear equation;

https://brainly.com/question/29739212

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katie has $120 on her cafeteria cardka. everytime she orders a meal , $4.50 is deducted from the

Answers

Answer:

120-4.50 = 115.10

Step-by-step explanation:

She will have $115.10 left if she buys one mean

Or if your question is how many meals can she get before she runs out of money in her account- your answer is 26 meals. 4.50*26= 117 so she would have $3 left over and not enough to buy her one more meal

What is the equation for the line?

Answers

Answer:it may be the first one but I can’t see the lines on the graph clearly.

Step-by-step explanation:

9+10
A.21 B.19 C.1 D.90

Answers

Answer: 19 XD

Step-by-step explanation: u add

Simplify the following expression............

PLEASE HELPPP! it’s due todayyyyy

Answers

The answer is 3k^2 m^6/ 4

You would put the first half on top of the four.

what is the value of 2.5x+17+21x-25=180

Answers

Answer:

x=8

Step-by-step explanation:

2.5x+17+21x−25=180

Simplify 2.5x+17+21x−25

23.5x−8=180

Move all terms not containing x to the right side of the equation.

23.5x=188

Divide each term by 23.5 and simplify.

x=8

Hope this helps! :) Plz mark as brainliest

What is 2/5 + 1/4+7/10

Answers

Answer:

1 7/20

Step-by-step explanation:

Answer:

27/20 or 1 7/20

Step-by-step explanation:

1) make the denominators the same

2/5 multiplied by 4 on top and bottom =8/201/4 multiply by 5 = 5/207/10 multiply by 2 = 14/20

2) add the numerators

8+5+14=27

3) the denominator stays the same

27/20

4) simplify it to 1 7/20

3) You paid $5 for a bucket of popcorn and $1.25 per candy bar. How many candy bars
can you buy to spend no more than $10?

Answers

4 dollars flat $4.00

Step-by-step explanation:

1.25x4= 5$ 5$+5$=10$

Answer:

4 candy bars

Step-by-step explanation:

you have to subtract $5 from $10, which is $5, then take the .25 from the candy bar. Add $4 candy bars to $5, $9, and then add in the .25. .25 times 4 is $1, and $9+$1 is $10

Choose the simplified form of the expression,
5x + 6x?- 2x + x
I need it fast please!!!

Answers

Answer:

10x

Step-by-step explanation:

If the question mark is an accident, the answer is 10x.

5x+6x-2x+x

11x-2x+x

9x+x

10x

Hi :)

First add 5x and 6x
5x + 6x = 11x

11x -2x + x

Combine 11x and -2x to get 9x

9x + x= 10x

Hope this helps!

Evaluate the expression of X = 3

Answers

Answer:

x=3

Step-by-step explanation:

x=3, there is no formula or anything...

What is the capital of peru

Answers

Answer:

☆<《HOPE IT WILL HELP YOU 》>☆

Step-by-step explanation:

capital of Peru is Lima

According to the U.S. Geological Survey, the Mississippi River is 200 mi
shorter than the Missouri River. Together, they cover a total of 4880 mi.
How long is the Missouri River? *

Answers

the answer would be 4,680 miles

Which best describes the solution set of the compound inequality below?

Answers

Answer:

Option B. 4<=x<=6 is the solution set.

is 4:3 and 3:4 equivalent

Answers

Answer: No

Step-by-step explanation:

sorry but nope...........
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