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

Factorise fully

gcse maths

please help

Answers

Answer:

Step-by-step explanation:

Numbers: HCF of 18 and 30

18: 2 * 3 * 3

30:2 * 3 * 5

HCF: 2 and 3 = 6

a: a * a and a.

HCF = a

b: b

c: c and c*c

HCF: C

Answer: 6*a*b*c(3a + 5*c)

Note: for this question one of the factors is the HCF and the other is what remains when the HCF is taken out.

answer the question in the picture

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Answer:

A and D

Step-by-step explanation:

Rational numbers that can be written as a fraction of two integers (without a denominator of 0).

The other three cannot be written as a fraction or two integers.

If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational. With that being said SQR 13 & 9 2/3 are rational.

100 PTS! HELP QUICK!!

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We have 7x - 3x - 2 + 1 = 8 + x - 3 - 3x
<=> 4x - 1 = 5 - 2x
<=> 4x + 2x = 5 + 1
<=> 6x = 6
<=> x = 1

Ok done. Thank to me:>

Answer:

x=1

Step-by-step explanation:

how to work out 12.5% of a number

Answers

Step-by-step explanation:

12.5÷100 × 5

=0.125×5

=0.625

quotient rule

fill in the blank


to divide two powers with the same base, ___ the exponent of the ______ from the exponent of the ______ and keep the same base

Answers

Answer:

add

subtract

multiply

Step-by-step explanation:

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

Find the ending balance if $500 was deposited at 5% annual interest compounded quarterly for 3 years.

Answers

Answer:

$575 ,

Step-by-step explanation:

5% of $500 is only $25

multiply that by 3YRS due to annual interest it would amount too

an addition $75 dollars so the answer is $575

I just need help simplifying

Answers

Answer:

(x - 2) / (x - 1)

Step-by-step explanation:

(x - 2)(x + 3) / (x - 1)(x + 3) <-- factor top and bottom

(x - 2) / (x - 1) <-- cancel out x + 3



Im pretty sure its
-1

Two​ trains, Train A and Train​ B, weigh a total of 436 tons. Train A is heavier than Train B. The difference of their weights is 242 tons. What is the weight of each​ train?

Answers

Answer:

Train A: 238    Train B: 194

Step-by-step explanation:

436-242=194-436=-238

Flip the sign for 238 and you get your answer.

(This might not be correct)

Also need this answer. Thank you so much!!!!!!!!

Answers

Answer:

5

Step-by-step explanation:

h(w)=2(1)+3

h(w)=2+3

h(w)=5

please give me brainliest think took some thinking

The area in square feet of a rectangular field is x^2-80x+1500. the width, in feet, is x-30. what is the length in feet.

Answers

Answer:

Step-by-step explanation:

Area = x² - 80x + 1500

        = x²  -30x - 50x + 1500

       = x(x - 30) - 50(x - 30)

        = (x -30) (x - 50)

Length =(x -50) ft

how do i solve -3x--3+8x-24=6x+7-5x

Answers

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

[tex]-3x--3+8x-24=6x+7-5x[/tex]

Two negative signs equate to a positive sign, so we can write [tex]--3[/tex] as just [tex]3[/tex]:

[tex]-3x+3+8x-24=6x+7-5x[/tex]

Add up similar terms:

[tex]5x-21=x+7[/tex]

Add 21 to both sides:

[tex]5x-21+21=x+7+21[/tex]

[tex]5x=x+28[/tex]

Subtract x from both sides:

[tex]5x-x=x+28-x[/tex]

[tex]4x=28[/tex]

Divide both sides by 4:

[tex]\frac{4x}{x} =\frac{28}{4}[/tex]

[tex]x=7[/tex]

(-5,1) and (-5,4) what is the slope of the line that passes through the given points

Answers

Answer:

Undefined

Step-by-step explanation:

I always like to take a good look at the points before I go about solving for the line. To me, it looks like this is going to be a vertical line. Why do I think that? Well, for each point, the x-value is -5. Since this is a linear function, every other point must also have an x-value of -5. So, our line would be straight up and down, going through the x-intercept (-5, 0). Let's try out this theory by subtracting our y-values and then our x-values, then dividing:

[tex]\frac{4-1}{-5-(-5)} =\frac{3}{-5+5} =\frac{3}{0}[/tex]

And that makes sense! Functions that show up as vertical lines are undefined, since their slopes always have 0 as a denominator, and anything divided by 0 turns out to be undefined. So, that's our answer - the slope is undefined.

Hopefully that's helpful! :)

Answer:

undefined

Step-by-step explanation:

(-5, 1) and (-5, 4) lie on the same vertical line.

A vertical line has undefined slope.

A population has a mean of 80 and a standard deviation of 6. A sample of 49 observations will be taken. What is the probability that the sample mean will be larger than 82

Answers

A population has a mean of 80 and a standard deviation of 6. A sample of 49 observations will be taken. What is the probability that the sample mean will be larger than 82

3. George is at the craft show selling homemade ice cream. He must pay

$45 for a booth rental and costs him $3.50 to make each Ice cream

cone. He sells each ice cream cone for $5.00.

The inequality 45 + 3.50c < 5c represents the situation in which George

makes a profit

a). Will George make a profit if he sells 29 cones? Explain why or why not.

Answers

Answer:

no 146.5 > 145

Step-by-step explanation:

Using the slope program, create the line y = 2x. Keeping the line the same, move one (or both) of the points so the triangle created by the points has a vertical length of 10 units. What is the horizontal length? Does this horizontal length match the answer you found in the previous question?

Answers

Answer:

x = 5 units

Step-by-step explanation:

Use the proportion we have to find the horizontal length:

y = 2x

When y = 10, the value of x is:

10 = 2xx = 10/2x = 5

[tex]\\ \sf\longmapsto y=2x[/tex]

Vertical length=yHorizontal length=x

Put y=10 in equation

[tex]\\ \sf\longmapsto 10=2x{/tex]

[tex]\\ \sf\longmapsto x=\dfrac{10}{2}[/tex]

[tex]\\ \sf\longmapsto x=5units[/tex]

HIGH POINTS/WILL MARK BRAINLIEST

Consider the leading term of the polynomial function. What is the end behavior of the graph?

2x^7– 8x^6– 3x^5– 3

Answers

Answer:

The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up.

Find the value of x in the equation below. 2.7+x=11.7

Answers

X=9 because 11.7-2.7= 9.

Have i done this right, why did i not get the third mark

Answers

Answer:

because you are good with math

Step-by-step explanation:

You are buying mouthwash at your local store. The price of the mouthwash is $4.39. It is currently on sale for 20% off. You also have a store coupon for $1.00 off and a manufacturer's coupon for $1.25 off. What is your subtotal?

Answers

Answer:5.68 dollars amirikan

Step-by-step explanation:

Given that price of the mouthwash is $4.39. It is currently on sale for 20% discount. You also have a store coupon for $1.00 off and a manufacturer's coupon for $1.25 off. The subtotal you need to pay is $1.262.

What is discount?

The term discount refers to the amount or percentage deducted from the normal selling price of something. The discount means a reduction in the price of a good or service.

Discount  = Marked price - Selling price

The mouthwash is at sale for 20% off.

Cost price = $4.39

Discount = 20% of $4.39 = $0.878

Total discount = 20% off + store coupon + manufacturer's coupon = $0.878 + $1.000 + $1.250 = $3.128

Selling price = Marked price - Discount = $4.39 - $3.128 = $1.262

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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

y=x-7
6x-6y=-7

elimination method

Answers

Answer:

The system has no solutions.

Step-by-step explanation:

Let's write it in a more traditional form

[tex]\left \{ {{x-y=7} \atop {6x-6y=-7}} \right. \\[/tex]

Try staring at it for a bit, and then realize what you are being asked: find two numbers whose difference is - at the same time, 7, and -7/6. That's impossible.

Same result you get by elimination. Multiply the first by 6 and either add or subtract - your choice the second. In either case you will get 0 = 35 or 0=49, which are obviously absurd

Suzanne has 15 books and will buy 3 more each month. Jack has 57 books and will sell 4 books each month. After how many months will they have the same number of books? How many will that be?

Answers

They would both have the same number of books after 6 months.

The number of books they would have is 33.

This expression can be used to determine the number of books Suzanne would have after x months: 15 + 3x

This expression can be used to determine the number of books Jack would have after x months: 57 - 4x

In order to determine the month in which both people would have the same number of books, equate both expressions.

15 + 3x = 57 - 4x

Combine similar terms

3x + 4x = 57 - 15

7x = 42

Divide both sides b y 7

x = 6

Number of books they would have : 15 + 3(6) = 15 + 18 = 33

A similar question was answered here: https://brainly.com/question/21014980?referrer=searchResults

solve pls brainliest

Answers

He will be paid $90 interest, but $690 in total

Simplify the scale 5mm: 1 meter , writing your answer in ratio form. ​

Answers

Answer:

1 : 200

Step-by-step explanation:

To get an answer in ratio form, we must convert meters into millimeters or we can convert millimeters to meters. Then we can get our answer.

Step 1: Convert.

=> 5 millimeters : 1 meter

=> 5 millimeters : 1000 millimeters

Step 2: Simplify.

=> 5 millimeters : 1000 millimeters

=> 1 millimeter : 200 millimeters

Key Note: Answer in ratio form is always unitless.

=> 1 : 200

So therefore, 1 : 200 is our ratio. Hoped this helped.

Please help asap!!!

Will give brainliest

Answers

Answer:

33/2 or

Step-by-step explanation:

2x−7

4

=

x+3

3

(2x−7)*(3)=(x+3)*(4)

6x−21=4x+12

Step 2: Subtract 4x from both sides.

6x−21−4x=4x+12−4x

2x−21=12

Step 3: Add 21 to both sides.

2x−21+21=12+21

2x=33

Step 4: Divide both sides by 2.

2x/2

=

33/2

x=

33/2

Answer:

  x = 33/2 = 16 1/2

Step-by-step explanation:

You can clear fractions first, or you can work with the fractions as is.

  (2x -7)/4 = (x +3)/3

  2/4x -7/4 = 1/3x +1 . . . . . eliminate parentheses

  (1/2 -1/3)x = 1 +7/4 . . . . . add 7/4 -1/3x

  1/6x = 11/4 . . . . . . . . . . . simplify

  x = 66/4 = 33/2  . . . . . multiply by 6, reduce the fraction

In a group of dogs and their owners, there are exactly 20 heads and 64 legs. How many dogs are in the group

Answers

Answer:

If we assume that everyone in the group is an owner, we would have

[tex]20*2=40[/tex] legs.

[tex]64-40=24[/tex] legs

Therefore, we need 24 more legs.

These 24 additional legs can be made from the difference of legs between the owners and dogs.

In this case, dogs have [tex]4-2=2[/tex] more legs than an owner.

24 ÷ 2 = 12.

There are 12 dogs in the group.

can y⁵ x y be simplified??​

Answers

Answer:

Yes,

[tex]y^{6} x[/tex]

Step-by-step explanation:

[tex]y^{5} xy = y^{5} *y*x = y^{6} x[/tex]

PLEASE HELPPP RUNNING OUT OF TIMMEE

Two shops sell baked beans in different sized tins. Calculate the price per 1.25 kg for shop B. Give your answer in pence.

Shop A) 1.25kg for £4.85
Shop B) 250g for £0.88

Answers

Step-by-step explanation:

you really need help with that ?

250g = 0.250kg = 0.25kg

comparing 0.25kg with 1.25kg : how many times of 0.25 is 1.25 ?

it is the same as with 25 to 125.

5 times !

so, you need to multiply the price also by 5 to get the price per 1.25kg :

0.88 × 5 = £4.40 = 440 pence per 1.25kg

Between what two whole numbers is 5/6 located on the number line? help please!

Answers

Answer:

Hello there!

5/6 is located between 0 and 1.

Step-by-step explanation:

5/6 is less than 1, because 1 = 6/6 in this scenario.

At the same time, it's greater than 0!

5/6 is located between 0 and 1 on the number line!

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