Each machine at a certain factory can produce 90 units per hour. The setup cost is 20 dollars for each machine and the operating cost is 26 dollars per hour (total, not 26 dollars per machine per hour). You would like to know how many machines should be used to produce 40000 units, with the goal of minimizing production costs.
First, find a formula for the total cost in terms of the number of machines, n:_______
TC = ______
machines for a total cost of The minimum total cost is achieved when using dollars.

Answers

Answer 1

Answer:

a)  [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

b)  [tex]n=24[/tex]

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]

Differentiating

[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]

Equating equ 1 to zero

[tex]0=\frac{20n^2+11556}{n}[/tex]

[tex]n=24[/tex]

Therefore

Substituting n

For Equ 1

[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]

F(n)>0  

For Equ 2

[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]

F(n)'<0


Related Questions

Answers plz fast ????? :D

Answers

Ans

Step-by-step explanation:

Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
9W + 1 = 19
9w =
Subtract 1 from both sides
W =
Divide both sides by 9

Answers

Answer:

see explanation

Step-by-step explanation:

9W + 1 = 19 ( subtract 1 from both sides )

9W = 18 ( divide both sides by 9 )

W = 2


A deposit of $1000 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the following sequence. Find the balance in the account after ten years.
a
=100.000)
n=1,2,3
The balance after ten years.

Answers

The balance after ten years is $2,208.04.

When an amount of money is compounded quarterly, it means that the amount deposited and the interest earns interest every quarter. The formula that can be used to determine the balance in 10 years is:

FV = P (1 + r)^nm

FV = Future value  P = Present value = $1000 R = interest rate = 8%/4 = 2% m = number of compounding = 4  N = number of years = 10

$1000 x (1.02)^40 = $2,208.04

To learn more about future value, please check: https://brainly.com/question/18760477

What is 12,925 to the nearest ten thousand

Answers

Answer:

To round to the nearest 10,000, you look at the number immediately to the right. If this number is 5 or above, you add 1 to the column in question and zero all numbers to the right. If the number immediately to the right is 4 or less, you just zero all numbers to the right.

In this case, the 10,000 column is the column with the 1. The number immediately to the right is 2. This is 4 or less, so we set all numbers to the right of the 10,000 column to zero.

I get 10,000

Step-by-step explanation:

10,000
Hope this helps!

PLEASE HELP RELATIONSHIPS IN TRIANGLES

Answers

Answer

TN=22

Step-by-step explanation:

You know that MT+TP+TN using the Orthocenter thereom.

help pls and thank you​

Answers

Answer:

A. $10

Step-by-step explanation:

They make $10 profit an hour.

n is m% of what?
It DEFINITELY a variable

Answers

Yes it is a variable because it’s a letter in a equation

4/k =8/3 ​ what is k?

Answers

Answer:

1.5

Step-by-step explanation:

4 x 2 = 8, so k x 2 = 3

3 / 2 = 1.5

A force of 18 lb is required to hold a spring stretched 2 in. beyond its natural length. How much work W W is done in stretching it from its natural length to 7 in. beyond its natural length

Answers

Answer:

Step-by-step explanation:

Average force is (19 + 0)/2 = 9 lb

2 inches = 1/6 ft

W = Fd = 9(1/6) = 1.5 ft•lb

The square below represents one whole.
What percent is represented by the shaded area?

Answers

40%
——————————————-

graph the relation y=2x

Answers

This is the graph for y= 2x

An airplane can ascend at a rate of 50 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?

Answers

Answer:

78.75

Step-by-step explanation:

A pianist charges $200 to perform at a restaurant. At the end of the night she collected her tips and left with a total earning of $310. Write an equation and solve for the amount she made in tips for the performance.

Answers

Answer:

310-200= T

Step-by-step explanation:

310 = 200 + x

Let’s break this down. 310 is their total earning, 200 is our set price for performing, and x represents how much she earned in tips.

310 = 200 + x

110 = x

Hope this helps!

A box contains 7 green marbles, 10 blue marbles, and 5 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that two of the marbles selected are green and the other marble is red.

Answers

Answer:

5/253

Step-by-step explanation:

The first green is 7/23, the second is 6/22 and the red is 5/21. Multiply them together for 5/253.

Question 10 of 10
To model some data, Pat ran an exponential regression and found the
regression equation to be y = 0.496.1.3%,
The scatterplot and residual plot are shown.
Scatterplot
Residual plot
y
4
2
Select the true statements.
O A. The model is a good fit because the patterns in the plots are both
curves.
B. The points in the scatterplot follow a line, so a linear model would
fit the data better.
O C. The residual plot changes direction, so a quadratic model would
fit the data better.
D. The model is not a good fit because there is a pattern in the
residual plot.

Answers

Answer:

B.)The points in the scatterplot follow a line, so a linear model would fit the data better

A.)The model is not a good fit because there is a pattern in the residual plot.

Step-by-step explanation:

The linear model would best fit the scatter plot while the quadratic model would fit the residual plot. The true statements are: B and C.

What is a Linear Model and a Quadratic Model?

A linear model is appropriate for data points that lie along a straight line on graph. If the line is not straight but curved and changes direction, a quadratic model is a better model for such data.

Thus, since the data points on the scatter plot are on a straight line, a linear model would fit the data.

For the residual plot that changes direction, a quadratic model would better fit the data.

The true statements are therefore: B and C.

Learn more about linear and quadratic model on:

https://brainly.com/question/13496810

#SPJ2

The following ordered pairs represent a function.
(-2,-4) (-1, -2) (0, 0) (1, 2) (2, 4)
Which two ordered pairs can be added to the given set and still have the set represent
a function?

Answers

Answer:

(-3,-6) and (3,6)

Step-by-step explanation:

First, use process of elimination on the answer choices with x coordinates already used in the relation, because a value of x cannot have 2 outputs, or y-values. This leaves you with 2 options. Hope I helped :D

Evaluate the function when x = -1,0, and 4.
9. g(x) = 3 -
X
g(-1) =
g(0) =
+
g(4) =



Plz help me I need the answer

Answers

G(-1) = 3/2
G(0) = 3
G(4) = 1

Function 1 is defined by the equation y=-1/4r-5

Answers

Step-by-step explanation:

and what is function 2 ?

but I think I can risk a guess based on the little piece of the graph I can see.

the y-intercept is simply the point on the y-axis (that means x=0), where the line crosses.

in other words, it is the y-value when x = 0.

the y-intercept of function 1 is therefore -5.

and the picture suggests that the visible line would cross the y-axis at about y=-6.

as -5 is greater than -6, function 1 has the greater y-intercept.

There are 4 dogs allowed at the park when there are 6 people. How many dogs are
there when there are 9 people?

Answers

Answer:

7

Step-by-step explanation:

since there are 4 dogs for every 6 people,

if we add 3 people, there will be 9 people and 7 dogs.

For lunch, I ate a toasted cheese sandwich and it has 450 calories and 16g protein with some baked potato fries and it has 230 calories and 3g protein. How much protein and calories did I eat in all?

Answers

Answer:

Give the person above me brainliest

Step-by-step explanation:

Martha has 2 apples if she buys 2 more how much does she have?

Answers

Answer 4
I Hope This Helps

Okie help please math math math

Answers

Answer:

x = 15

Step-by-step explanation:

The angles shown are supplementary angles. Supplementary angles add up to equal 180°

This means that 2x + 8 + 8x + 22 must equal 180

Note that we've just created an equation that we can use to solve for x

We now solve for x using that equation

2x + 8 + 8x + 22 = 180

combine like terms : 2x + 8x = 10x and 8 + 22 = 30

10x + 30 = 180

subtract 30 from both sides : 30 - 30 cancels out and 180 - 30 = 150

10x = 150

divide both sides by 10: 10x / 10 = x and 150 / 10 = 15

we're left with x = 15

Answer:

x = 15

Step-by-step explanation:

The angles shown are supplementary angles. Supplementary angles add up to equal 180°

This means that 2x + 8 + 8x + 22 must equal 180

Note that we've just created an equation that we can use to solve for x

We now solve for x using that equation

2x + 8 + 8x + 22 = 180

combine like terms : 2x + 8x = 10x and 8 + 22 = 30

10x + 30 = 180

subtract 30 from both sides : 30 - 30 cancels out and 180 - 30 = 150

10x = 150

divide both sides by 10: 10x / 10 = x and 150 / 10 = 15

we're left with x = 15

Mary had 60$ and spent 3/4 on a coat. plus she brought a skirt with 1/2 she had left . how much do she have left?

Answers

3/4 of $60 = $45 for the coat
60 - 45 = $15 left
1/2 of $15 = $7.50 for the skirt
15 - 7.50 = $7.50 left

I need help with this question

Answers

Answer:

check online for more information

A courtyard has the shape of a rectangle 45 ft and 28 ft wide. How long is a sidewalk from one corner diagonally to the opposite corner?
56 ft

47 ft

50 ft

53 ft

Answers

Answer:

53

Step-by-step explanation:

We use the pythagorean theorem, a^2 + b^2 = c^2. We can fill a and b for 45 and 28. 45^2 is 2025, and 28^2 is 784. Adding them up gives us 2809. The square root of 2809 is 53.

Please helpppp quick

Answers

Answer:

x<-4

Step-by-step explanation:

The arrow shows an open circle around -4 meaning it's not equal to -4. And we see the arrow going left, meaning x<-4.

Hope this helps :^)

Answer:

x<-4

Step-by-step explanation:

There is an open circle where -4 is, so the maximum would be -5. There would be no minimum, so you can say that x is less than -4.

Help use photo for questions

Answers

the rise is -6 the run is 3 rise/run

y=-6/3

What is the next whole number after 267 In base 8

Answers

The next number would be 270₈. The given number has an digit expansion of

267₈ = 2•8² + 6•8¹ + 7•8⁰

If x is the next number, then adding 1 to the both sides gives

x = 2•8² + 6•8¹ + 7•8⁰ + 1

x = 2•8² + 6•8¹ + 7•8⁰ + 1•8⁰

x = 2•8² + 6•8¹ + 8•8⁰

x = 2•8² + 6•8¹ + 1•8¹

x = 2•8² + 7•8¹

x = 2•8² + 7•8¹ + 0•8⁰

and so x = 270₈.

Integrate:Cos 7x/(1+sin**2(7x))​

Answers

Answer:

7x/1+7sin(2)x

Step-by-step explanation:

How do u write x/7=14 in algebra tiles

Answers

Answer:

98 is the answer.

Step-by-step explanation:

x/7 = 14

=> 14 × 7 = 7 × x/7

=> x = 98

Therefore, 98 is the answer.

Hoped this helped.

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