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

Read more at:

brainly.com/question/25471478


Related Questions

37,162 Divided by 10 to the third power equals what

Answers

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

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.

i need answers thank you

Answers

The correct answer is A) y=-2x

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

hope this helps☆☆

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!

#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

Please answer all of the above thanks ur the best!:)
and please explain how u got the answer on each question! thanks
1. 2 1/3 + 1 3/4

Answers

Answer:

4.0833333

Step-by-step explanation:

PLZ give brainliest thanks

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

[tex]20(\frac{11}{4})=55\\20(2.75)=55[/tex]

fill in the blank to make the fractions equivalent.
4/5 ?/15​

Answers

Answer:

12/15

Step-by-step explanation:

times 4 by 3 because 5 is timesed by 3

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

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.
• B. No, because it is not a straight line.
O C. Yes, because it passes the vertical line test.

Answers

Answer:

c

Step-by-step explanation:

C, because a vertical line will only hit the function on one point at a time.

Answer:

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

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

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

Answers

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:

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:

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!

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.​

Answers

Answer:

Step-by-step explanation:

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.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

The equivalent ratios are 6 : 2, 3 :
,
: 4, 15 :
.

Answers

Answer:

Hi freind just it

Step-by-step explanation:

A sphere has a radius of 4 inches. Determine the effects on the surface area and volume of a sphere when the radius is changed.

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

At r = 4":

A = 64π in^2

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:

4":  (85.3π in^3)/(64π in^2) = 1.33   [(1/3)r = 4/3 = 1.33]

5":  (167π in^3)/(100π in^2) = 1.67   [(1/3)r = 5/3 = 1.67]

V/A = (1/3)r

Since Volume is a function of r^3 and Area is related to r^2, Volume will always increase faster, by a ratio of 1/3 r.

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

Write the standard form of the equation of the circle with a radius of 7 and center (2,-4).


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


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


(x+2)2+(y-4)2=7


(x-2)2+(y+4)2=7

Answers

( x - 2 )² + ( y + 4 )² = 49

.........................................

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

PLEASE HELP I need the answer please ​

Answers

17. <

18.=

19.>

20.>

21.3.021,3.12,3.121,3.21

22. 1.03,1.03,1.3,1.39

23.

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

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.

Answers

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:

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 please :) I’m quite stuck on this one

Answers

Answer:

-4-4i

That's the answer for the question

I don’t understand can someone tell me the answer

Answers

Answer:

12>x>10

Step-by-step explanation:

-25<-3x+5

-3x+5<-31

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

Graph the lines y=3x+3

Answers

~graph

Graph the line using the slope and y-intercept, or two points.

Slope : 3

y intercept = (0 , 3)

graph already attached ✔️

~ nice to help you ^^

Answer:

Step-by-step explanation:

Other Questions
The symbol delta x (x) is used to find what value? five friends get together to have a thanksgiving dinner. roger, ted, tom, pam, and donna brought (in no particular order) turkey, salad, dressing, peas, and potatoes. each item was brought on a different colored plate (no particular order) white, purple, black, green, and pink. - no food begins with the same letter as the name of the person who brought it- the dressing was not brought by tom or pam- the person who brought the potatoes and the person who brought the green plate both have names that begin with the same letter- neither rogers plate nor teds plate was purple and the peas were also not brought on the purple plate- toms food and the food on the pink plate are not peas or potatoes- donna did not bring the black platetry to determine the kind of food each person brought and what color plate it was on determining that the amount of cash agrees with the accounting records describe how you know this is a proportional relanshoships Find the value of y when x=-44. 1/3y=2(x-1/6) 5. -6x-y=17.75 If given a chance to focus on just three level of peace. What is it and why? A ski resort is building two parallel straight ski slopes for children. One of them has a gradient of 1/3. The other ski slope will pass through points (2,-3) and (s,-5). Find the value of s For f(x) = -5x+10, what us the value of x for which f(x) = 35 When 8 goes in,5 comes outWhen 24 goes in.13comes outwhen 70 goes in,__ comes outWhat is the missing answer? HELP IM TIMED!!!!!!!!!!Question 2(Multiple Choice Worth 5 points)(MC)STORIES OF USEFUL INVENTIONS, excerptBy S. E. Forman1911THE MATCHThere never was a time when the world was without fire, but there was a time when men did not know how to kindle fire; and after they learned how to kindle one, it was a long, long time before they learned how to kindle one easily. In these days we can kindle a fire without any trouble, because we can easily get a match; but we must remember that the match is one of the most wonderful things in the world, and that it took men thousands of years to learn how to make one. Let us learn the history of this familiar little object, the match.Fire was first given to man by nature itself. When a forest is set on fire by cinders from a neighboring volcano, or when a tree is set ablaze by a thunderbolt, we may say that nature strikes a match. In the early history of the world, nature had to kindle all the fires, for man by his own effort was unable to produce a spark. The first method, then, of getting fire for use was to light sticks of wood at a flame kindled by natureby a volcano, perhaps, or by a stroke of lightning. These firebrands were carried to the home and used in kindling the fires there. The fire secured in this way was carefully guarded and was kept burning as long as possible. But the flame, however faithfully watched, would sometimes be extinguished. A sudden gust of wind or a sudden shower would put it out. Then a new firebrand would have to be secured, and this often meant a long journey and a deal of trouble.In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate of potash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggist had discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemical because it is made by mixing certain chemicals together and rubbing them. Although Walker's match did not require the bottle of acid, nevertheless it was not a good one. It could be lighted only by hard rubbing, and it sputtered and threw fire in all directions. In a few years, however, phosphorus was substituted on the tip for antimony, and the change worked wonders. The match could now be lighted with very little rubbing, and it was no longer necessary to have sandpaper upon which to rub it. It would ignite when rubbed on any dry surface, and there was no longer any sputtering. This was the phosphorus match, the match with which we are so familiar.What is the main idea of this text?A. Firebrands were hard to keep lit.B. Nature provided fire to early humans.C. The history of the match is interesting.D. The match made life easier for humans. _______ is the process of translating thoughts into a code or language that can be understood by others. What is polytheism? brainliest you A and B are complementary. mA=29. find mB. Why is Mustafa Kemal Ataturk important to the history of Turkey?a) He was the 10th heir apparent.b) He separated religion and politics in the Turkish government.c) He invented the technique of Iznic tiles.d) He conquered Constantinople from the Christians. Which sense is used to determine whether an object is something you might want to eat?smellsighttasteall of the above 1. Jim Crow laws were used to integrate the South.a. Trueb. False2. The Chinese Exclusion Act allowed Asians to enter the U.S. only through Ellis Island.a. Trueb. False Define the sample space, S, of a fair coin being tossed once.S=A. {H, T}B. {H, H}C. {T, T} Please help me this is due tomorrow. What is the difference between obtaining molecules from food and air in a water bear from obtaining the same by a human body? (need 3 sentences) who knows, please help The Batpod and The Falcon Cycle are traveling down thehighway. That Batpod can travel at a speed of 4 milesper minute; while the Falcon Cycle can double that at aspeed of 8 miles per minute. If Falcon gives Batman a 6minute head start. How long will Batman have traveledbefore Falcon catches him?I need help so I can turn in my Packet?!?!?