Consider the following.

P = −0.1s3 + 6s2 + 400.

Required:
a. Find the amount s of advertising (in thousands of dollars) that maximizes the profit P (in thousands of dollars).
b. Find the point of diminishing returns.

Answers

Answer 1

Answer:

A) s = $40 (in thousands of dollars)

B) point of diminishing returns is at;

(20, 2000) in thousands of dollars

Step-by-step explanation:

We are given the profit function as;

P = −0.1s³ + 6s² + 400

A) To maximize the profit, we need to find the first derivative and equate it to zero.

Thus;

dP/ds = -0.3s² + 12s

At dP/ds = 0, we have;

-0.3s² + 12s = 0

0.3s² = 12s

0.3s = 12

s = 12/0.3

s = $40 (in thousands of dollars)

B) To find the point of diminishing returns, we need to find the 2nd derivative of the given profit function and equate to zero.

Thus;

d²P/ds² = -0.6s + 12

At d²P/ds² = 0, we have;

-0.6s + 12 = 0

0.6s = 12

s = 12/0.6

s = 20

At s = 20,

P = −0.1(20)³ + 6(20)² + 400

P = -800 + 2400 + 400

P = 2000

Thus; point of diminishing returns is at;

(20, 2000) in thousands of dollars


Related Questions

You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?

Answers

Given:

You are given $893 in one, five, and ten dollar bills.

There are 165 bills.

There are twice as many five dollar bills as there are ones and tens combined.

To find:

How many bills of each type are there?

Solution:

Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.

According to the question,

Number of bills : [tex]x+y+z=165[/tex]         ...(1)

Total amount : [tex]1x+5y+10z=893[/tex]         ...(2)

Condition : [tex]y=2(x+z)[/tex]     ...(3)

Equation (3) can be written as

[tex]\dfrac{y}{2}=x+z[/tex]       ...(4)

Substituting [tex]x+z=\dfrac{y}{2}[/tex] in (1), we get

[tex]\dfrac{y}{2}+y=165[/tex]

[tex]\dfrac{3y}{2}=165[/tex]

[tex]3y=330[/tex]

[tex]y=110[/tex]

Substituting y=110 in (4), we get

[tex]x+z=\dfrac{165}{2}[/tex]

[tex]x+z=55[/tex]

[tex]x=55-z[/tex]       ...(5)

Substituting y=110 and x=55-z in (2), we get

[tex](55-z)+5(110)+10z=893[/tex]

[tex]55-z+550+10z=893[/tex]

[tex]9z+605=893[/tex]

[tex]9z=893-605[/tex]

[tex]9z=288[/tex]

Dividing both sides by 9, we get

[tex]z=32[/tex]

Substituting z=32 in (5), we get

[tex]x=55-32[/tex]

[tex]x=23[/tex]

Therefore,

One dollar bills = 23

Five dollars bills= 110

Ten dollars bills = 32

What number must be added to 101 to produce a number equal to the product of 101 x 21

Answers

Answer:

2020

Step-by-step explanation:

101 • 21 = 2121

2121 - 101 = 2020

Please help
Trying to help daughter do virtual. And I stink in this stuff!
w(t) = 3t – 1; t = 5

Answers

The answer is W =14/5 I believe

When five times a number is decreased by 9​, the result is 11. What is the​ number?

Answers

Answer

4

Step-by-step explanation:

Add 9 to 11, then divide that by 5.

Answer:

4

Step-by-step explanation:

work backwards 11+9 is 20. Divide 20 by 5 = 4

The living room of Ann's house is a square with an area of 121 square feet. What is the length of each side of the foyer

Answers

Answer:

30.25

Step-by-step explanation:

121 divided by 4 is 30.25

Perform the indicated operation

3/4 divided by 1/3

Answers

Answer:

2 1/4

Step-by-step explanation:

3/4 ÷ 1/3 = ?

(to divide fractions faster you flip the second fraction so:)

3/4 x 3/1 = 2 1/4

simplify these numbers
1. 125 5. 384
2. 458 6. 15710
3. 438 7. 2549
4. 10512 8. 8920

Answers

1. how do i simplify them like in fractions?

help me please !!!!!!!

Answers

Answer:

I don't see the screenshot and i'm not going to download it...

Step-by-step explanation:

yikes

Please help me with this!
I will give you a thanks!

Answers

-2 + 6
.................
-2+6 . Count the spaces . That’s what I used to do

8 groups of ___ hundredths is 0.32

Answers

Answer:

the answer is 0.4 The reason is because 0.4 x8=0.32

Step-by-step explanation:

4x+2 = 2(2x+1) what is the answer?

Answers

Answer: 0=0

Step-by-step explanation: Simplify

PLEASE HELP!!! Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, l and the number of hours clearing tables, c, that Chloe can work in a given week.

Answers

Answer:

got u homie

Step-by-step explanation:

Answer:

l +c _> 12

Step-by-step explanation:

Sharon went bowling with her friends. She paid $3 to rent
her shoes and then $3.75 for each game (x) of bowling. She
spent a total of $18. How many games did she bowl?
WRITE YOUR EQUATION:
SOLVE:
SOLUTION:

Answers

Answer:

3 + 3.75x=18

subtract 3 from both sides

3.75x=15

divide by 3.75 on both sides

x=4

Step-by-step explanation:

what is 8 times 0.9 equal

Answers

Answer:

7.2

Step-by-step explanation:

Simplify (-4/5)divided by (3/-2). -8/15 -6/5 6/5 8/15

Answers

Answer:

8/15

Step-by-step explanation:

-4/5 ÷ -3/2

Copy dot flip

-4/5 * -2/3

Multiply the numerators

8

Multiply the denominators

15

Put the numerator over the denominator

8/15

Answer: 8/15

Step-by-step explanation: (-4/5)divided by (3/-2) is 8/15.

2+2=4 because 2 fingers and then another 2 fingers

Answers

Answer:

yes

Step-by-step explanation:

Answer:

yes? That's right. ummmm lol

Blood pressure: High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.4. A sample of 39 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. Part: 0 / 60 of 6 Parts Complete Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure? It ▼(Choose one) appropriate to use the normal curve, since =np ▼(Choose one)10 and =n−1p ▼(Choose one) 10.

Answers

Answer:

Yes it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure

Step-by-step explanation:

From the question we are told that

The population proportion is  p=0.4

  The sample size is  n =  39

  The sample proportion is  [tex]\^ p = 0.43[/tex]

Generally for normal approximation to be used

       [tex]np > 10[/tex]

so np  =  39 * 0.4 =  15.6 > 10

   and [tex]n(1- p) > 10[/tex]

so   n(1-p ) = 39(1-0.4) = 23.4 >10

Given that the both condition is meet it mean that  it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure

Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?
O Scale z by the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.

Answers

Answer: C

Step-by-step explanation:

I just took the quiz and I got it right

Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

What is Complex number?

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit

What is Modulus of a complex number?

Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin

Given,

Complex number z divides by a second complex number w

To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction

From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w

Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

Learn more about Complex number and Modulus of a complex number here

https://brainly.com/question/19554199

#SPJ2

67

Name

_Michael Goodger Lesson 4 Homework

1.Convert and write an equation with an exponent.

A. 2 meters to centimeters

2m = 200 cm

2 x 10 = 200

B. 108 centimeters to meters 108 cm = 1 m

1.08% 101=108

C. 2.49 meters to centimeters 2.49 m = 249

cm

2.49x 103= 249

D. 50 centimeters to meters 50 cm = 1 m

50x1=50

E 6.3 meters to centimeters 6.3 m = 63 cm

6.3x63=63

F 7 centimeters to meters Icm = _

m

In the space below, list the letters of the problems where smaller units are converted to larger units.

2. Convert using an equation with an exponent. Use your meter strip when it helps you.

a. 4 meters to millimeters

mm

b. 1.7 meters to millimeters

mm

1050 millimetorn

m =

m =

Answers

Answer:

Step-by-step explanation:

1)

A. 2 meters to centimeters

1 m = 100 cm

[tex]2 m = 2 \times 100 \\2 m = 200 cm = 2 \times 10^2[/tex]

B)108 centimeters to meters

100 cm =1 m

[tex]1 cm = \frac{1}{100} m \\108 cm = \frac{108}{100}=108 \times 10^{-2} m[/tex]

C)2.49 meters to centimeters

1 m = 100 cm

[tex]2.49 m = 2.49 \times 100 = \frac{249}{100} \times 100 = 249 cm[/tex]

D)50 centimeters to meters

100 cm = 1m

[tex]1 cm = \frac{1}{100} m \\50 cm = \frac{50}{100}= 5 \times 10^{-1} m[/tex]

E)6.3 meters to centimeters

1 m = 100 cm

[tex]6.3 m = 6.3 \times 100=\frac{63}{10} \times 100 = 630 cm[/tex]

F)7 centimeters to meters

100 cm = 1 m

[tex]1 cm = \frac{1}{100} m\\\\7 cm = \frac{7}{100} = 7 \times 10^{-2} m[/tex]

2)

a)4 meters to millimeters

1 m = 1000 mm

[tex]4 m = 4000 = 4 \times 10^3 mm[/tex]

b)1.7 meters to millimeters

1 m = 1000 mm

[tex]1.7 m = 1.7 \times 1000= \frac{17}{10} \times 1000=17 \times 10^2 mm[/tex]

Help me with this question pleasee

Answers

Answer:

√23 = a

Step-by-step explanation:

/ab/²= /ac/²+/bc/² (Pythagoras theorem)

12² = a² +11²

144 = a² + 121

144 - 121 = a²

23 = a²

√23 = a

Read 3 integer numbers from the user; these numbers represent the lengths of 3 straight lines. From the 3 lengths, determine whether a triangle can be formed with the corresponding lines. If it is possible to form a triangle, determine whether the triangle is a right triangle or not. The rules to be used are: 1. To form a triangle where all lines’ ends meet (form vertices), the sum of the lengths of two sides must be greater than the length of the third side. This short video illustrates this concept: How to determine if the three sides make up a triangle. 2. Per the Pythagorean theorem: in a straight triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. 3. The user can enter the lengths of each line in any order, i.e.: you may not assume that the first length is the longest or the smallest or the middle value.

Answers

Answer:

Written in Python

print("Enter three sides of a triangle: ")

length = []

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

length.sort()

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

    print("Triangle")

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

else:

    print("Not Triangle")

Step-by-step explanation:

This line prompts user for sides of triangle

print("Enter three sides of a triangle: ")

This line declares an empty list

length = []

The following iteration gets user input

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

This line sorts user input

length.sort()

The following if condition checks if user input is triangle

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

The following is executed is the if condition is true

    print("Triangle")

The following if condition checks if user input forms a right angled triangle

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

This is executed if user input is not a triangle

else:

    print("Not Triangle")

Help me plz
It’s 8th grade math
And ion know what the answer is..

Answers

Answer:

B slope = 1 and y intercept is 3

Step-by-step explanation:

The y intercept is where the line crosses the y axis (x is zero).

The slope can be figured by how far the line rises and runs to the next intersection of lines. In this case it goes up 1 and to the right 1. The slope would be 1/1 or 1

Answer:

Slope =1 ; Y-intercept=3

Step-by-step explanation:

The y intercept would be the point on the vertical line that touches the graph which in this case is three.

then to get to the next point that's on the line would have to move over 1 once to the right and one time up. so the slope is 1 over 1 which would equal 1.

The scatterplot and trend line show a positive correlation between advertising costs and sales.
Which two points can be used to find the slope of the trend line?

Point 1: ?
Point 2: ?

Answers

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

What is |-24| + |13| =?

Answers

Answer:

37

Step-by-step explanation:

just add the two numbers like they are not negative.

Identify the terms, coefficients, and constants in the expression.
7h + 3
I need help now!!!!!

Answers

Step-by-step explanation:

7 is the coeffiecient

3 is the constant

Calculate.
(2x105)(4.3x109)
Write your answer in scientific notation.

Answers

Answer:

9.8427x10⁴

Step-by-step explanation:

Answer:

98427x^2

9.8427x10^4

Step-by-step explanation:

Number 10 plzz???????

Answers

%error=(6.5g/mol - 7g/mol)/(7g/mol) * 100= 7.14% error

Help ill give brainliest
Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.

4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?

A. The equation has one solution: x = 0.
B. The equation has one solution: x = 8.
C. The equation has no solution.
D. The equation has infinite solutions.

Answers

The equation has B. no solution

Answer:

C. no solution

Step-by-step explanation:

3x – 4 = 3x + 4

3x-3x=4+4

0=8

which is not possible.

So, it has no solutions.

w(t) = 3t – 1; t = 5

Answers

I’m not sure if your asking for the solution, but Hope this helps!

How many 2/3 cup servings are in 28/3 cups of yogurt

Answers

The answer fam is..... 14

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