A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, consumers will buy approximately 160y/(y+4)+170x/(x+7) units of the product.

If manufacturing costs for the product are 130 dollars per unit, how much should the manufacturer spend on development and how much on promotion to generate the largest possible profit?

Round your answer to the nearest dollar.
Development costs: $ ?
Promotion costs: $ ?

Answers

Answer 1

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757


Related Questions

Solve:
y = 4x
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Answer:

15 is the answerof this question

Triangle XYZ is reflected across the y-axis, and X = (4, –5). What are the coordinates of X’ ?
(–5, 4)
(–4, –5)
(4, 5)
(–4, 5)

Answers

Answer:B

Step-by-step explanation:I looked it up, I don’t copy people’s answers ok don’t flame me in comments.

The coordinates of X in triangle XYZ after reflection across the y axis is X' = (-4, -5)

Transformation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation

If a point A(x, y) is reflected over the line y axis, the new point is at A'(-x, y).

Triangle XYZ is reflected across the y-axis, and X = (4, –5). Hence X' = (-4, -5)

Find out more on Transformation at: brainly.com/question/1462871

8y-5< 3


Solve the inequality. The solution is _____.

Answers

Answer:

Use Photo Math, it will explain all of the steps

2. Sara started out with $50 in her piggy bank. Every week she deposited the same amount of
money in the bank. After 7 weeks she had $67.50. Find the average rate of change or slope
in dollars per week. (This is a unit rate.)

Answers

Answer:  2.5 dollars/week

Step-by-step explanation:

50 + 7x = 67.50               x is the cost she deposited every week

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x = 2.5

Which expression represents the distance between -3 and 5 on the number line?
- 3+5
-3-5
1-3+51
1-3-51

Answers

The expression that represents the distance between -3 and 5 on the number line is “-3-5”.

Answer:

B

Step-by-step explanation:

Which of the following values for x and y make the equation 4x + 2y + 3 = 19 true? ​

Answers

Can I get a bran list please
A. X=5 4(5)+2y+3=19 y=-7
B.x=4 4(4)+2y+3=19. Y=0
C.x=3 4(3)+2y+3=19 Y=2
D.x=2 4(2)+2y+3=19 y=4
From the calculations the above only the third choice has a similar value of y to the value in calculations
The answer is letter C

Someone please explain this it’s confusing me.

Answers

Answer:

x = 4 radical 3 / 3

Step-by-step explanation:

this is a 30-60-90 triangle

the side across from the angle 30 is L

the side across from the angle 60 is L√3

the side across from the angle 90 is 2L

we are given the side across from 60⁰ so we know that:

2 = L√3

we want to solve for L, so we must divide both sides by √3 (radical three)

2/√3 = L√3/√3

you would get 2/ √3 = L, because the radical three cancels out on the L side.

but you can't have a radical in the denominator, so you have to multiply 2/√3 by radical 3

2 times √3 and √3 times √3

you get 2√3/√9

radical nine can simplify

2radical3/3 or 2√3/3

we found L, but that would equal the thirty degree angle, not the 90, 90 = 2L

multiply the number infront of the radical by two and get

4√3/3

x=4 radical 3 divided by 3

What quantity of 61% hydrochloric acid solution must be mixed with a 21% hydrochloric acid solution to produce 277.5 mL of 53% solution?

Answers

Answer:

222 mL

Step-by-step explanation:

okay so lets multply them lets call the quantity of hydrocloric acid x

so 61x+ 21(277.5-x)= 53*277.5

61x+ 21*277.5-21x= 53*277.5

40x=(53-21)(277.5)

40x= (32)(277.5)

x= 222 mL

if my answer helps please mark as brainliest.

1. Marisol is making a pattern with blocks. What might the missing shape be? First, look at the blocks. ? Shape: 1 1 . 2 3 Next, describe Marisol's pattern.​

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Answer:

edwardrocks124531

Beginner

2 answers

4 people helped

Answer:

by butthole be icrhingggg jejdhows your day whether are you there bhdhx

Step-by-step explanation:

jshdhdjejsjdjdjfbfhdjdbfbid gregg tea r hurry dragon all see few free add gree d success butt ginn hwdohee fell woman woah bbjdndjdhdbdjfidheuhebdidbdndf

Step-by-step explanation:

7 David spent 2 2/5 hours reading on Saturday night. On Sunday, he spent 3 1/5 hours reading. How much time did he spending reading on Saturday and Sunday?* (10 Points) O 54/5 hours A 5 3/5 hours 6 hours 075/5 hours Next​

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Answer:

5 and 3/5

Step-by-step explanation:

For this problem, they are asking that we basically sum up the total amount of reading time on Saturday and Sunday. Saturday's reading time is 2 and 2/5, while Sunday's reading time is 3 and 1/5. Add them together to get 5 and 3/5.

HELP ASAP! I’m very confused and need help!

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Answer:

I think it's 1 and 7 and 2 and 8.

Step-by-step explanation:

^^

24. On the coordinate plane to the right, graph
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Help fast pls

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I have no idea what this answer is sorry

5th grade math. correct answer will be marked brainliest.

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Answer:

The answer will be 41/14

Step-by-step explanation:

2.928571429

Find the sum: (n + 7) + (n - 14)

Answers

Answer:

2n - 7

Step-by-step explanation:

To get the sum you would combine like terms.

So:

n + n= 2n

7 + -14 = 7 - 14 = -7

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2n - 7

PLEASE HELP HELP HELP IMAGE ATTAcHED

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Answer:

is 3

Step-by-step explanation:

because look at the down the trigal and you will see that they pointing at the tree

Answer:

3

Step-by-step explanation:

P(1, 3) ⇒ P'(3, 9)

R(1, 1) ⇒ R'(3, 3)

Q(3, 1) ⇒ Q'(9, 3)

Looking at the points, it appears that the x and y coordinates are being multiplied by 3. Therefore, the scale factor is 3.

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the last one

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Answer:(12 cm) x (7 cm) x (6 cm) x 8.4 =

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A truck can drive 200 kilometers on 25 liters of gasoline.
How many liters of gasoline do I need to drive 640 kilometers?
imut How many hours will it

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80 liters of gasoline
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Answer:

y=1/2x-2

Step-by-step explanation:

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m=(-1-1)/(2-6)

m=-2/-4

m=1/2

y-y1=m(x-x1)

y-1=1/2(x-6)

y=1/2x-6/2+1

y=1/2x-3+1

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Logx(x-3)=1 solve for x

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Answer:

I think the 1st one would be 10...

Step-by-step explanation:

Because 12-2=10 and 18-8=10.

If I'm wrong, im super sorry

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C I believe that it is C also I have bad period cramps send chocolate
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build the graph of the equation (x-2)(y-3)=0

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Step-by-step explanation:

Rick earned $24 for each car he washed. This month he washed 15 cars. He spent $85 of the money he earned this washing cars and saved the red of the money. How much money did Rick save from the he earned washing cars this month?

Answers

Answer:

$275

Step-by-step explanation:

If you multiply 24 by 15 you get the total which is $360. When you subtract the $85 he spent you get $275 left over that he is saving.

56 + -90 * 2 - -17 =

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Step-by-step explanation:

Help a friend in need

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a) 4.71ft

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Step-by-step explanation:

Perimeter is 1/2 the circumference

1/2 Circumference = 2*pi*radius

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Radius = 3/2 = 1.5ft

Circumference = 2*pi*1.5ft = 9.42

1/2 Circumference = 4.71

4.71ft is the perimeter.

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A = 7.065ft^2

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Write 9/12 as a sum of unit fractions.

Answers

Answer:

9/12 = 1/2 + 1/4

Step-by-step explanation:

This can be done in an unlimited number of ways. Which you choose depends on what you are trying to achieve. Each way will get you the same sum. <33

can you write equivalent fractions for 2 1/5 and 1 and 5/6 using 30 of the common denominator ​

Answers

Answer:

yes   they would be 1 25/30  and  2 6/30

Step-by-step explanation:

The equivalent fractions for 2 1/5 and 1 and 5/6 using 30 of the common denominator would be 1 25/30  and  2 6/30

What is a fraction?

A fraction has two parts: Numerator and Denominator.

It is in the form of a Numerator / Denominator. A fraction is a numerator divided by the denominator.

We need to write equivalent fractions for 2 1/5 and 1 and 5/6 using 30 of the common denominator .

Now consider the first fraction as;

2 1/5 = 11/5

Then other fraction must be multiple of the denominator of the other.

So, 1 and 5/6 = 11/6

We can see that "the denominator of one is a multiple of the denominator of other" that is 5 x 6 = 30

Thus the two fractions are; 1 25/30 and 2 6/30

Learn more about fractions here:

brainly.com/question/10354322

#SPJ2

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Answer:

x=-12

Step-by-step explanation:

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