A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-10x^2+600x-3588
y=−10x
2
+600x−3588

Answers

Answer 1

Answer:

Step-by-step explanation:

The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:

[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and

[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.

x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.

Our variables for the quadratic are as follows:

a = -10

b = 600

c = -3588. Therefore,

[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:

[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:

[tex]k=-3588-(\frac{360000}{-40})[/tex] and

k = -3588 - (-9000) and

k = -3588 + 9000 so

k = 5412

That means that the profit made by selling the widgets at $30 apiece is $5412.

Answer 2

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

What is the maximum profit?

Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.

Here given that,

A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.

As the maximum profit found in the vertex of the parabola,

Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.

The number of items sold is [tex]x[/tex].

So, the quadratic equation is:-

[tex]a = -10b = 600c = -3588.[/tex]

Therefore, so the cost of each widget is $[tex]30[/tex].

For the profit:-

[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

To know more about the maximum profit

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Related Questions

3 ÷ 6/7 i really need help! i will give you brainliest pls HELP​

Answers

Answer:

7/2

Step-by-step explanation:

---------------------------------------------------------

3.5

---------------------------------------------------------

(30 POINTS NEED HELP FAST)
A line has a slope of 2 and goes through the point (4,−3). What is the equation of this line in Standard Form?

−2x+y=−5

2x+y=−5

−2x+y=5

−2x+y=−11

Answers

Answer: −2x+y=−11

(4,-3) = −2x+y=−11.

Answer: −2x+y=−11.

Help please zearn is so hardddd

Answers

Answer:

1000-20

Step-by-step explanation:

The table shows the makeup of a New Year’s Eve television show. What fraction of the show will be for the audience to speak?
Table:
Introduction: 10%
Skits: 25%
Guests: 45%
Audience: 20%

Answers

Answer:

1/5

Step-by-step explanation:

We need to find the fraction of the show will be for the audience to speak. Here, the part of the audience is 20%.

We know that, percent means we need to divide the value by 100 i.e.

[tex]20\%=\dfrac{20}{100}\\\\=\dfrac{2}{10}\\\\=\dfrac{1}{5}[/tex]

So, the required fraction is 1/5.

Main Menu
Solve the equation
Unit 2
- 8c+7= -25
Section 3.2
Section 3.3
Section 9.3
Section 9.5
Section 9.6

Answers

Answer:

c = 4

Step-by-step explanation:

Solve for"c" in the following equation:

- 8 c + 7 = - 25

Subtract 7 from both sides:

- 8 c = - 25 - 7

combine like terms

- 8 c = -32

divide both sides by "-8" to isolate c on the left

c = - 32 / (-8)

c = 4

78 feet wide and 27 feet long what is the perimeter?

Answers

Answer:

105

Step-by-step explanation:

When finding the perimeter add them together

4.20. According to a report released by the National Center for Health Statistics, 51% of U.S. households has only cell phones (no land line). According to the FCC, nearly 70% of the U.S. households have high-speed Internet. Suppose of the U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected. a. What is the probability that the household has only cell phones and has high-speed Internet

Answers

Answer:

The probability that the household has only cell phones and has high-speed Internet is 0.408

Step-by-step explanation:

Let A be the event that represents U.S. households has only cell phones

Let B be the event that represents U.S. households have high-speed Internet.

We are given that 51% of U.S. households has only cell phones

P(A)=0.51

We are given that 70% of the U.S. households have high-speed Internet.

P(B)=0.7

We are given that U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected.

P(B|A)=0.8

[tex]\frac{P(A\capB)}{P(A)}=0.8\\P(A\capB)=0.8 \times P(A)\\P(A\capB)=0.8 \times 0.51\\P(A\capB)=0.408[/tex]

Hence the probability that the household has only cell phones and has high-speed Internet is 0.408

Every day you collect 8 pennies and keep them in a jar. The first day you have 8, the second day you have 16, etc. How many pennies do you have on the 113th day?​

Answers

Answer:

904

Step-by-step explanation:

8 x 113 = 904

I think it is 904
Hope this helps!!!!!

231km 118m - 485km 829m in the smallest unit

Answers

Answer:

Uhhhhhh

Step-by-step explanation:

ABUNDA LA CACA BDHDHENSNGAGVD

Answer:

hard

Step-by-step explanation:

Micah found the least common multiple of 8 and 12. His work is shown below.

Multiples of 8: 8, 12, 16, 20, 24, 28, . . .
Multiples of 12: 12, 24, 36, 48, 60, . . .

The least common multiple is 12.

What is Micah’s error?

Answers

Answer:when he was doing the multipleis of 8 he put 20 when there is no 20

Step-by-step explanation:

He forgot the 20 when he was doing the 8

Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 – 4i and Tomas has a score of 3 + 2i, what is their total score?

Answers

Answer:

8 - 2i

Step-by-step explanation:

Just add the real parts together and then add the imaginary parts together

5 + 3 = 8

-4i + 2i = -2i

8 - 2i

Answer:

8-2i

Step-by-step explanation:

Can somebody please help me with this math problem

Answers

Answer:

According to the question 25% of the students wore jackets.

Thus 25% of 12 wore jackets

The number of students can be found easily by multipling 12 with 25//100

12*25/100

12*1/4

12/4

thus, 3 students

Therefore, option 3 is correct

Given that a=4,b=2 and c=-1, find the value of a-b+c

Answers

Answer:

1

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

a - b + c

a = 4

b = 2

c = -1

Step 2: Solve

Substitute:                         4 - 2 - 1Subtract:                            2 - 1Subtract:                            1

please help asap :)​

Answers

The answer to this question is “No”

can yall help me out please.​

Answers

Answer:

which one equals 12? option C

Step-by-step explanation:

g Suppose you are rasterizing a triangle with vertices (1, 1), (5, 1), and (2, 9), and the intensity values (e.g., redness) of those vertices are 5, 9, and 14, respectively. Using the linear interpolation scheme, what is the intensity value of an interior point at (3, 5)? Show all your work.

Answers

Answer:

6.333

Step-by-step explanation:

Our triangle vertices are

(1,1)(5,1)(2,9)

We are to perform interpolation at point(3,5)

x and y values are interpolated

On vertices (5,1)(2,9)

x = 3

x1 = 5

X2 = 2

Y1 = 1

Y2 = 9

Formula for interpolation

Y = [y1+(x-x1)(y2-y1)]/x2-x

Y = 1+(3-5)(9-1)/2-5

Y = 1+[-2*8/-3]

Y = 1+16/3

From here we use use LCM to get:

19/3 = 6.333

Please help me everyone!
In Kennington, 25 legislators represent 500,000 people.
Kennington has 2,500,000 people. How much legislators do they need?
Please help, I repeat.

Answers

                                                  [tex]\huge\boxed{125.}[/tex]

[tex]\boxed{-------------------------------------}[/tex]

Explanation...

So, 25 legislators represents 500,000 people.

We are trying to find how much legislators you need to represent 2,500,000.

500,000*5=2,500,000.

25*5=125.

Therefore, your answer is 125.

[tex]\boxed{-------------------------------------}[/tex]

Hope i helped!

[tex]\huge\boxed{Thanks,Plip.}[/tex]

Answer: 125

In Kennington, 25 legislators represent 500,000 people.

Find how many times 500,000 go into 2,500,000 people.

2,500,000 ÷ 500,000 = 5

Now, multiply 5 by 25, because each 500,000 people are represented by 25 legislators.

25 x 5 = 125.

Answer = 125.

Hope this helps you!

Sammy wants to buy a new mattress priced at $419. He enters into an agreement to pay $26 a month for 24 months. How much will the finance charge be for this purchase?

Answers

If Sammy pays a monthly installment of $ 27 for 24 months, then the total amount paid by Sammy is 24 * $ 27 = $ 648. Now, since the

9.831 rounded to the nearest tenth

Answers

Answer:

9.8

Can i get brainliest please?

Answer:

9.8

Step-by-step explanation:

Hoped that helped :)

PLS HELP QUICKLY WILL GIVE BRAINLIEST

Answers

Answer:

the first one

Step-by-step explanation: it is your answer because when you solve it i gt that answer i calculated it in a calculator and then showed to the teahcre and said that it was crrect please mark me as brainlist

PLEASE ANSWER QUICKLY I WILL MARK BARINLIEST AND WILL GIVE
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Answers

Look up decimal to percentage calculator and you can enter the decimals and get your answer because me entering all of them would be a pain

Can someone answer this and explain how to solve the 3 with the exponent of -4?

Answers

Answer:

3⁷

Step-by-step explanation:

When you multiplying or dividing numbers with exponents, you keep the base the same and specifically with dividing, you subtract the exponents themselves. So, you would be doing 3-(-4), which is 7.

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Exponents and power,

Since we know the concept that, any power in denominator of a fraction is shows as negative power when it comes to the Numerator of the fraction,like eg:-

[tex]1 \div ( {5}^{8} ) = {5}^{ - 8} [/tex]

so we apply here same,

also

[tex]1 \div ({5}^{ - 8} ) = {5}^{8} [/tex]

so we get as,

[tex] {3}^{3} \div {3}^{ - 4} = {3}^{3} \times {3}^{4} [/tex]

this is the answer.

Sandra is making decorations for the school dance out of construction paper. Each decoration uses 223 2 2 3 sheets of paper. Sandra notices that she only has 1012 10 1 2 sheets left.

Answers

Answer:

Step-by-step explanation:

CACA POOP

Answer:

464

Step-by-step explanation:

hwe

Is the product of 0.4 * 1.8 greater then or less then 0.4


Answers

Answer:

Greater

Step-by-step explanation:

.4*1.8 is .72

.72 is greater than .4

PLEASE HELP!?!?!

a. c + 7 less than or equal to 3


b. c – 3 > 1


c. c – 7 < 3


Matching


Match the inequality to the graph of its solution.

Answers

It’s b hope that helped have a great night

Find the measures of the missing values.

Answers

1. X and Y= 39 (180-102=78, 78 divided by 2=39)

The width of a rectangle is 1 ft less than the length. The area is 30 ft2. Find the length and the width.

Answers

Answer:

the anwer is 5*6

What is
41/6
as a mixed number in simplest form?
Enter your answer in the box.

Answers

Answer:

6 1/6

Step-by-step explanation:

six goes into 42 seven times that leaves you with one number so it can go in six times evenly and that leaves you with 1/6

The answer is as a mixed number is 6 1/6

Find the x- and y-intercepts of the graph of the linear equation −4x+3y=−30

Answers

Answer:

y-int = -10, x-int = 15/2

Step-by-step explanation:

y int:

-4(0)+3y=-30

3y=-30

y=-10

x int:

-4x+3(0)=-30

-4x=-30

x=30/4=15/2

Solve the system of equations: y=x^2, y=x+6

A.(3,9)
B.(-3,9),(2,4)
C. (-2,4),(3,9)
D.(-2,-4),(3,9)

Answers

The answer is C. (-2,4), (3,9)
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