1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gavmur [86]
2 years ago
10

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

s 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: $ ?
Mathematics
1 answer:
sattari [20]2 years ago
3 0

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

You might be interested in
The questions are in the pic the other answer is 356
Andru [333]
The answer to this question is 356
4 0
3 years ago
What is the answer 2c+(3c-4)=a-4
gavmur [86]

Answer:idk

Step-by-step explanation:

5 0
3 years ago
Danielle put 4.902 gallons of gasoline in a gas tank. What is 4.902 written in expanded form?
evablogger [386]
4.902 written in expanded form is A
3 0
3 years ago
Read 2 more answers
What is the slope equation? Drag and drop answers
zubka84 [21]

Answer:

y = 2x + 9

Step-by-step explanation:

The y-intercept: 9

Slope: 2x

3 0
3 years ago
Can u plz help and thank u​
tatiyna
The answer is 396

Area = base x height
Area = 44 x 9
396 = area
5 0
3 years ago
Read 2 more answers
Other questions:
  • A newspaper conducted a survey to find out how many high school students play video games.The two ways table below displays the
    11·1 answer
  • A quadrilateral has angles that measure 63°, 89° and 121°.
    13·1 answer
  • Name each of the following for the circle!!! all radi, diameter, chords
    15·1 answer
  • -2r – 5a + 12r + 10 + 5a. HELP ASAP
    8·1 answer
  • In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio
    12·1 answer
  • Sarah converts the number 1,500,600 into scientific notation. She writes 1.5006 x 104. Which of the following statements is true
    10·1 answer
  • PLEASE BE QUICK!!! 15 POINTS!!! What is the area of the triangle QRS?<br><br> _______ square units
    10·2 answers
  • Which is greater 4.08 or 4.1
    6·2 answers
  • Please help lol and thank u
    12·2 answers
  • What is the height of a rectangle with an area of 105 and a base of 15
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!