A company makes a profit of $y (in thousand dollars) when it produces x computers, where y is given by the formula = ( − 100)( − 200) for ≥ 0 If 120 computers are produced, the profit will be $3,200,000.
a) Find the value of a.
b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?
(7 marks) c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?

Answers

Answer 1

lol no

just give up in life

Answer 2

The function is used to model real life situation

The value of a is -2000 150 computers must be produced to maximize the profit of $5,000,000 A range of 140 to 160 computers would give the company at least $4,800,000  

 

(a) The value of a

The function is given as:

[tex]\mathbf{y = a(x - 100)(x - 200) }[/tex]

The profit on 120 computers is 3200000.

So, we have:

[tex]\mathbf{3200000 = a(120 - 100)(120 - 200) }[/tex]

[tex]\mathbf{3200000 = -1600a}[/tex]

Divide both side by -1600

[tex]\mathbf{a = -2000}[/tex]

Hence, the value of (a) is -2000

(b) The maximum profit

The function becomes

[tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

Expand

[tex]\mathbf{y = -2000(x\² - 200x - 100x + 20000)}[/tex]

[tex]\mathbf{y = -2000(x\² - 300x + 20000)}[/tex]

Expand

[tex]\mathbf{y = -2000x\² + 600000x - 40000000}[/tex]

Differentiate

[tex]\mathbf{y' = -4000x + 600000}[/tex]

Set to 0

[tex]\mathbf{-4000x + 600000 = 0}[/tex]

Collect like terms

[tex]\mathbf{4000x = 600000}[/tex]

Divide both sides by 4000

[tex]\mathbf{x = 150}[/tex]

Substitute 150 for x in [tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

[tex]\mathbf{y = -2000(150 - 100)(150 - 200)}[/tex]

[tex]\mathbf{y = 5000000}[/tex]

150 computers must be produced to maximize the profit of $5,000,000  

c) Range when the target is at least $4,800,000

This means that:

[tex]\mathbf{y \ge 4800000}[/tex]

So, we have:

[tex]\mathbf{-2000x\² + 600000x - 40000000 \ge 4800000}[/tex]

Collect like terms

[tex]\mathbf{-2000x\² + 600000x - 40000000 - 4800000 \ge 0}[/tex]

[tex]\mathbf{-2000x\² + 600000x - 44800000 \ge 0}[/tex]

Divide through by -2000

[tex]\mathbf{x\² - 300x +22400 \le 0}[/tex]

Factorize

[tex]\mathbf{(x - 140)(x - 160) \le 0}[/tex]

Express as inequality

[tex]\mathbf{140 \le x \le 160}[/tex]

A range of 140 to 160 computers would give the company at least $4,800,000

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Related Questions

What is the equation of the line from the graph?​

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Answer:

y=3

Step-by-step explanation:

All points have the same y coordinate. Or

A line parallel to the x axis has slope 0, so it's y= 0x +3 that becomes y=3

Answer: Y=3

Step-by-step explanation:

Does this graph represent a function? Why or why not?
D. Yes, because it is a curved line.
O A. No, because it fails the vertical line test.
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c

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Answer:

C. Yes, because it passes the vertical line test.

Of the houses in Kimberly's neighborhood, 5/12 are pink and another 1/3 are red. What fraction of the houses are either pink or red?

Answers

Answer:9/12

Step-by-step explanation:

You need to make the denominators the same. Multiply the 1/3 by 4 and now you are ready. You add 4/12 and 5/12 together. 9/12 houses on her block are pink/red. You can also simply it down to 3/4.

If 11 - 3x = x, then 20x=

Answers

Answer:

20x = 55

Step-by-step explanation:

First you have to add 3x to both sides of 11-3x=x

[tex]11-3x=x\\+3x=+3x\\11=4x[/tex]

Now that you have 11 = 4x you divide 4 on both sides [tex]\frac{11}{4} =\frac{4x}{4}[/tex]

11/4 = x

But you can't divide 11 by 4 unless you are looking for the decimal form of 11/4 which is 2.75

so now we take 11/4 or 2.75 depending on if you need your answer in fraction or as a decimal and replace that with x  however both will equal the number 55

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Can someone please give me examples of linear, quadratic, Absolute value, square root, cubic, cube root, exponential, logarithmic, and rational function (parent function) equations to help my friend? Please and thank you. I'll give brainliest to the first person who does all of them and get them right.

Answers

Answer:

Step-by-step explanation:

Consider the cube root parent function.

( graph in photo below )

Complete the statements to make them true.

A cube root function will ( 1 ) ________ have an x-intercept and ( 2 ) ________ have a y-intercept.

For the parent cube root function, ( 3 ) ____________ located at .

Answer:

1. always

2. always

3. both intercepts are

the explination photos below

Answer:

I got you

[tex]f(x)=3x+2[/tex]

[tex]f(x)=4x^2+3x+7[/tex]

[tex]f(x)=|x+4|[/tex]

[tex]f(x)=\sqrt{x+12}[/tex]

[tex]f(x)=6x^3+4x^2-3x-5[/tex]

[tex]f(x)=\sqrt[3]{3x-5}[/tex]

[tex]f(x)=2^x[/tex]

[tex]f(x)=log_3(x)[/tex]

[tex]f(x)=\frac{x+5}{x-3}[/tex]

Each function is respective to the order of the list given.

Let me know if you want the graphs

Choose the statement that correctly compares their unit rates. A. Tyrone's unit rate is equal to John's unit rate. B. Tyrone's unit rate is 2 more miles per hour than John's unit rate. C. Tyrone's unit rate is 1 more mile per hour than John's unit rate. D. Tyrone's unit rate is 1 fewer mile per hour than John's unit rate.​

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Answer:

Step-by-step explanation:

i need answers thank you

Answers

The correct answer is A) y=-2x

Subtract the equations.
3x + 4y = 17
(3x +2y = 3)
-
O A. 6x = 20
O B. -6x = 14
c. 2y = 14
O D. 6y = 20

Answers

Answer:

C

Step-by-step explanation:

The perimeter of a scalene triangle is 14. 5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6. 2 cm? A scalene triangle where all sides are of different lengths. The base of the triangle is labeled 2a, is twice that of the shortest side labeled a. The other side is labeled b. Choose the correct answer.

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I know u felt offend and I love you so much so much love and hope that not everyone else is going to accept that as a result I am now in a person

Answer:

9.3+ b= 14.5

Step-by-step explanation:

I don’t understand can someone tell me the answer

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Answer:

12>x>10

Step-by-step explanation:

-25<-3x+5

-3x+5<-31

10.
Peter is 1.64 metres tall.
Peter is 18 centimetres taller than Nick.
San
Work out Nick's height in metres.

Answers

Answer:

the height of nick is 1.46

Step-by-step explanation:

because to change cm into m we need to divide it by 100so 18/100is 0.18

and total height of Peter is 1.64 so if we -the 0.18then we can get nick's height

Answer:

1.46

Step-by-step explanation:

1.64 to cm is 164

164-18 = 146

146 to meters is 1.46

Evaluate the following expression
a+b divide c
when:
a = 2
b= -3
C= -1
d=5
Show your work by substituting and solving.

Answers

Answer:

1

Step-by-step explanation:

a+b divide c -> [tex]\frac{a+b}{c}[/tex]

Plugging in - > [tex]\frac{2+-3}{-1}[/tex]

Simplifying: [tex]\frac{2-3}{-1}[/tex]

Subtracting: [tex]\frac{-1}{-1}[/tex]

Simplifying: 1

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The total student at Shiloh middle school is 1,400 students. If the ratio of boy to girls is 3:4 for the school how many students are boys and how many students are girls

Answers

ANSWER:

There are 600 boys and 800 girls.

SOLUTION:

We are given the following facts:

The total number of students is 1,400.The ratio of boys to girls is 3:4.

We express this as a partitive proportion.

» Solve for x.

[tex] \sf 3x + 4x = 1400 [/tex][tex] \sf 7x = 1400 [/tex][tex] \sf x = \frac{1400}{7} [/tex][tex] \sf x = 200 [/tex]

Now we to solve for the number of boys and the number of girls.

» Number of boys:

= [tex] \sf 3x [/tex] = [tex] \sf (3)(200) [/tex] = [tex] {\boxed{\sf 600}} [/tex]

» Number of girls:

= [tex] \sf 4x [/tex] = [tex] \sf (4)(200) [/tex] = [tex] {\boxed{\sf 800}} [/tex]

Thus, there are 600 boys and 800 girls. The sum of these is the total number of students in Shiloh Middle School.

HOPE IT HELPS!

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Answers

Answer:

Step-by-step explanation:

The surface area of a sphere is given by

A=4πr^2

The volume is

V = (4/3)πr^3

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V = 85.3π in^3

At r = 5" (a 25% increase in r)

A = 100π in^2  (a 156.25% increase)

V = 167π in^3  ( a 195.8% increase)

We can show the ratio of these two measures by dividing the Volume by the Area:

V/A = ((4/3)πr^3/(4πr^2))

V/A = (1/3)r

For the 2 examples (4" and 5"), V/A is:

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17. <

18.=

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20.>

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23.

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Answers

Answer:

12/15

Step-by-step explanation:

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(x-2)2+(y+4)2=49


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Answers

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Answer:

-4-4i

That's the answer for the question

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Answer:

37.162

Step-by-step explanation:

We know that 10 to the third power is 10³ = 1000. When a number is divided by 1000, the decimal point is moved 3 digits to the left. Therefore, we can get 37,162/1000 = 37.162

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Hi freind just it

Step-by-step explanation:

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Answers

~graph

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graph already attached ✔️

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Answer:

Step-by-step explanation:

Adam has some marbles.
Bradley has twice as many marbles are Adam.
Chris has 5 more marbles than Bradley.
In total they have 55 marbles.
How many marbles does Chris have?

Answers

Answer:

Chris has 25 Marbles

Step-by-step explanation:

If Adam starts with 10, Bradley will have twice as many, meaning Bradley's amount is 20. Making the new total, 30 Marbles. Chris has 5 More Marbles than Bradley, making Chris have 25 Marbles. If you add the total's up, you get 55 Marbles in total.

Hope this helps!!

Help!!! I will give brainliest if correct!!!
Ken Has k video games, and Jeff has j video games. If Ken gives 6 video games to Jeff, Ken will have twice as many video games as Jeff. Which equation shows the relationship between k and j?
A: k-6 = 2(j + 6)
B: k - 6 = 2j + 6
C: 2(k - 6) = J
D:2(K - 6) = J + 6

Answers

Answer:

D

Step-by-step explanation:

2(k-6)=J+6

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Answer:

4.0833333

Step-by-step explanation:

PLZ give brainliest thanks

Please arrange these numbers in descending order for me
7.23, 7.32, 7.3, 73

Answers

Answer:

73

7.32

7.23

7.3

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answer this asap


1)There are 30 students in a class. 18 are girls. Express the number of girls as a percentage of the
class.

2)What is the probability of choosing the color blue from the colors of the rainbow?

Answers

Answer:

1) 18/30×100%=60%

Hope this helps!!!

Answer:

See below

Step-by-step explanation:

Hi there!

Question 1

There are 30 students in total and 18 are girls, making 18/30 of the class girls. To express this as a percent, divide, then multiply by 100:

18/30 = 0.6

0.6 × 100 = 60%

Therefore, 60% of the class is girls.

Question 2

There are 7 colours in the rainbow, making blue 1/7 of the colours of the rainbow.

Therefore, the probability of choosing blue from the colours of the rainbow is 1/7.

I hope this helps!

a plumber who is just starting out offers low rates to attract new customers. He charges $35
to visit a client's home, plus an additional $20 per hour.
Write an equation that shows how the cost of a visit, y, depends on its duration in hours, X.

Answers

Answer:

y=20x+35

Step-by-step explanation:

if a plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. Then y=20x+35 is equation that shows how the cost of a visit, y, depends on its duration in hours, X.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that

a plumber who is just starting out offers low rates to attract new customers

Plumber charges $35 to visit a client's home, plus an additional $20 per hour.

Let the charges per hour be denoted by x.

and it is given that y is cost of a visit.

We are required to write equation for cost of a visit y.

y equal to twenty x plus thirty five.

y=20x+35

Hence if a plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. Then y=20x+35 is equation that shows how the cost of a visit, y, depends on its duration in hours, X.

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group of 3 people is going on a boat tour. If each boat holds 3 people, how many will boats will the group need?

Answers

Answer:

1

Step-by-step explanation:

there are 3 people and 1 boat holds three people

#3) Find the measure of arc N).


Answers

Answer:

Arc NJ is 65°

Step-by-step explanation:

An entire circle measures 360°

Therefore, add all the given dimensions and subtract the sum to 360

> 150+50+50+45 = 295

> 360-295 = 65

Therefore, the measurement of arc NJ is 65

Find the value of x and 3x.
x=
3x=

Answers

Answer:

Step-by-step explanation:

Sum of all the angles of the polygon = (n -2) *180  

                                                             = (6 - 2) * 180 = 4 *180 = 720

45 + 135 + 45 + 135 + x + 3x = 720

          360 + 4x = 720

                     4x = 720 - 360

                    4x = 360

                       x = 360/4

x = 90

3x = 3*90 = 270

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