Prove that the EOQ cost function can be rewritten as
g(Q) = h/2 * Q(Q - underroor 2K/h) + underroot 2Kh
Use this to prove without using calculus.

Answers

Answer 1

Answer:

the EOQ cost function [tex]\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}[/tex]

Step-by-step explanation:

Given that:

[tex]g(Q) = \dfrac{h}{2 \lambda Q} \begin {pmatrix} Q- \sqrt{\dfrac{2 K \lambda}{h}} \end {pmatrix}^2 + \sqrt{\dfrac{2 Kh}{\lambda}}[/tex]

Total cost = Purchase Cost + Ordering Cost + Holding Cost

i.e

T = [tex]P \lambda + h \dfrac{Q}{2}+\dfrac{\lambda K}{Q}[/tex]

By differentiating with respect to Q and equating to zero, we have:

[tex]0 = 0 +\dfrac{h}{2}- \dfrac{\lambda K}{Q^2}[/tex]

[tex]Q* = \sqrt{\dfrac{2 k \lambda}{h}}[/tex]

Now;

[tex]T = P \lambda + \dfrac{h}{2Q}(Q-Q^*)^2 + hQ^*[/tex]

[tex]T = \dfrac{h}{2Q}(Q- \sqrt{\dfrac{2 \lambda K}{h}})^2 + \sqrt{2 hK \lambda } + P \lambda[/tex]

[tex](\dfrac{T - P \lambda}{\lambda }) = \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}[/tex]

Therefore:

the EOQ cost function [tex]\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}[/tex]


Related Questions

WILL GIVE BRAINLIEST WORTH THIRTY POINTS! Find a so that CD will have the given slope: a) C(5,−2), D(−4,a); m=0 b) C(a,–1), D(–3,2); m=undefined c) C(–3,–2), D(1,a); m=2

Answers

The value of a for the equation of line CD are;

a) a = -2b) a = -3c) a = 6

Given the following data:

a) C(5, -2), D(-4, a); m = 0

Point on x-axis ([tex]x_{1}, x_{2}[/tex]) = [tex]5, -4[/tex]Point on y-axis ([tex]y_{1}, y_{2}[/tex]) = [tex]-2, a[/tex]Slope, m = 0

To find the value of a;

Mathematically, the slope (m) of an equation of line is given by the formula;

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the values into the formula, we have;

[tex]0 = \frac{a - [-2]}{-4 - 5}\\\\0 = \frac{a\; + \;2}{-9}[/tex]

Cross-multiplying, we have;

[tex]-9[/tex] × [tex]0[/tex] = [tex]a + 2[/tex]

[tex]a +2 = 0[/tex]

a = -2

b) C(a, -1), D(-3, 2); m = undefined

Point on x-axis ([tex]x_{1}, x_{2}[/tex]) = [tex]a, -3[/tex]Point on y-axis ([tex]y_{1}, y_{2}[/tex]) = [tex]-1, 2[/tex]Slope, m = undefined

To find the value of a;

Note: Undefined is a terminology used to refer to a mathematical expression that has not been assigned a value or isn't correct. Also, a mathematical expression is considered to be undefined when its denominator is zero (0) i.e it is divided by zero (0).

Substituting the given values into the slope formula, we have;

Undefined [tex]= \frac{2 - [-1]}{-3 - a}[/tex]

Undefined [tex]= \frac{2 + 1}{-3 - a}[/tex]

Next, we would equate the denominator to zero (0);

[tex]-3 - a = 0[/tex]

a = -3

c) C(-3, -2), D(1, a); m = 2

Point on x-axis ([tex]x_{1}, x_{2}[/tex]) = [tex]-3, 1[/tex]Point on y-axis ([tex]y_{1}, y_{2}[/tex]) = [tex]-2, a[/tex]Slope, m = 2

Substituting the values into the formula, we have;

[tex]2 = \frac{a - [-2]}{1 - [-3]}\\\\2 = \frac{a\; + \;2}{1 \;+ \;3}\\\\2 = \frac{a\; + \;2}{4}[/tex]

Cross-multiplying, we have;

[tex]4[/tex] × [tex]2[/tex] = [tex]a + 2[/tex]

[tex]a +2 = 8[/tex]

[tex]a = 8 -2[/tex]

a = 6

Find more information on slope here: https://brainly.com/question/19131126

Y=BD-5, for B. solve for B​

Answers

Answer:

Step-by-step explanation:

BD - 5 = Y

BD = Y + 5

B = (Y + 5)/D

y=BD-5
5+y=BD
B=D(y+5)

translate into words

Answers

b . Square root of 25

What’s the perimeter of a rectangle 47ft 57ft

Answers

Answer:

The perimeter is (47x2)+(57x2). So the answer is 208ft

Step-by-step explanation:

PLEASE HELP!!!!!!!
What is the absolute value of |-1||?
Use this number line to determine the absolute value.
t
-2
0
wint
win
1
3
-3
WIN+
2
3

Answers

Answer:

The answer is 1 ⅓

Step-by-step explanation:

Anything in an absolute value whether negative or positive will always end up being a positive

Levi prepares 3 kilograms of dough every hour he works at the bakery. How many hours did Levi work if he prepared 27 kilograms of dough?

Answers

Answer:

1 hour = 3 kg

27 ÷ 3 = 9 hours

hope this helps.

Find the quotient: –10/19÷(−5/7)

Answers

Answer:

14/19

Step-by-step explanation:

Note that there are two " - " signs here.  Thus, the end result will be " + "

We move from left to right, obtaining first 10/19 divided by (5/7):

10

----- ÷ (5/7)

19

To divide by (5/7), invert (5/7) and then multiply.  We get:

10      7      2(7)

----- * ----- = ------- = 14/19

19       5       19

twelve thousand four hundred three in standard form

Answers

Answer:

12,403

Step-by-step explanation:

twelve thousand = 12,000

four hundred = 400

three = 3

Add them all up.

Your answer is 12,403.

Hope this helps!

Answer: 12,403

twelve thousand = 12,000

four hundred = 400

three = 3

The answer is 12,403. Hope this helps!

Today, you worked from 7am to 4pm. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember, 30 minutes is equal to .5 hours.

Answers

Answer:smbhaISHBIA

Step-by-step explanation:

ahbkjbajbsx

Over the last 3 months, you deposited $600 each month into your business checking account. During that time, you
withdrew $1,208.23 to make purchases. What is the net change in your account balance?
O -$3.008.23
O $608.23
$591.77
O $1,808.23
$3.008.23
Intro
Done

Answers

Answer:

591.77

Step-by-step explanation:

we multiply 600 by 3 to get 1,800 then subtract 1,208.23 from 1,800 to get 591.77

PLEASE HELP !
The equation 8(u+3)=-16 is solved in several steps below. For each step , choose the reason that best justifies it

Answers

Answer:

Division property of equality

Step-by-step explanation:

Answer:

I hope this picture helps tho!!

Find the LCM of 30 and 22. LCM = ___a0

Answers

Answer:

The answer would be 330:)

Step-by-step explanation:

How to Find LCM by Listing Multiples :

List the multiples of each number until at least one of the multiples appears on all lists

Find the smallest number that is on all of the lists

This number is the LCM

RLY hope this helps:) If so, can I have brainliest?

Answer:

The LCM of 30 and 22 is 330

Step-by-step explanation:

22 x 15 = 330

30 x 11 = 330

An online test of English spelling looked at how well people spelled difficult words. The bar graph to the right shows how many people per 100 spelled each word correctly. a. Estimate the number of people per 100 who spelled weird correctly. Round to the nearest 5. b. In a group consisting of 8724 randomly selected​ people, estimate how many more people can correctly spell weird than inoculate.

Answers

Answer:

a). 85 people

b). 4362 people

Step-by-step explanation:

The given bar graph shows how many people per 100 spelled each word correctly.

a. From the graph given extreme end of the bar for the word "weird" is between 80 - 90.

Therefore, approximate number of the persons who spelled weird correctly will be 85 (rounded to the nearest 5).

b. The number of people who can correctly spelled word "weird" = 85

The number of people who can correctly spelled word "inoculate" = 35

In 100 people, number of people who can correctly spell "weird" more than "inoculate"

= 85 - 35

= 50

in a group of 8724 randomly selected people, number of people who can spell the word "weird" correctly more than "inoculate"

= [tex]\frac{50}{100}\times 8724[/tex]

= 4362 people

The number of people per 100 who spelled weird correctly is 85 rounded to nearest 5. In a group consisting of 8724 randomly selected​ people, 4362 people can correctly spell weird than inoculate.

Random selection means each individual has equal chance of being selected.

Given graph has the following information:

Total number of people under survey=100

a. To estimate the number of people per 100 who spelled weird correctly

From the graph it is around 84 and rounding it to nearest 5 will results in 85.

b. From the graph,

Number of people can correctly spell inoculate= 35

Number of people can correctly spell weird than inoculate=85-35

=50 out of 100

Using unitary method as follows:

100-------->50

1------------>1/2

8724------>1/2x8724

=4362

Thus, out of  8724 randomly selected​ people, 4362 people can correctly spell weird than inoculate.

Learn more about random selection, here:

https://brainly.com/question/33537473

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Questions in the picture. Pls help!!!!!

Answers

A=5
B=3
C=5
D=3
hope that helps (:

Answer:

A = 5

B = 3

C = 5

D = 3

Step-by-step explanation:

A - B = 2

• 5 - 3 = 2

A + C = 8

• 5 + 3 = 8

A + C = 10

• 5 + 5 = 10

B + D = 8

• 5 + 3 = 8

Paul has 16 fish pictures and 12 deer pictures. He wants to arrange the pictures in rows with the same numbers of fish and of deer pictures in each row. What are the possible numbers of rows

Answers

Answer:

4 rows

Step-by-step explanation:

GCF of 12 and 16 is4

Kendall scored 3 times as many points as Abdul scored in a basketball game. Otis scored 5 more points than Abdul scored. The three players scored 45 points all together. How many points did each player score?

Answers

Answer:

Kendall: 24

Abdul: 8

Otis: 13

explanation:

24 is 3x more than 8 and 13 is 5 greater than 8

Answer: Kendall: 24 points; Abdul: 8 points; Otis: 13 points

Step-by-step explanation:

K= 3A

O= A = 5

O + A + K = 45

Paige can run one lap around a track in 3 1/5 minutes. How long would it take her to run 6 1/2 laps?

Answers

1 lap equals to 3 1/5 minutes what about 6 1/2 cross multiply to get 6 1/2*3 1/5 divide by 1 you get 20 4/5 translated to time is 20 minutes and 48 seconds (4/5*60=48)
20 minutes 48seconds

Dimensional Analysis How many seconds old are you if your 16 yrs old? show work

Answers

Answer:

504,576,000

Step-by-step explanation:

16 years x 365 days x 24 hours x 60 minutes x 60 seconds = 504576000

Find MN.
2x - 16
X-9

Answers

Answer:

3

Step-by-step explanation:

LN = 11

x - 9 + 2x - 16 = LN add like terms

3x - 25 = 11

3x = 36

x = 12

MN = x - 9 therefore MN = 3

find the total pay for the week $12.50 per hour time and a half for sunday hours worked day must be rounded to the nearest quarter hour.

Answers

Answer:

  $392.19

Step-by-step explanation:

I find it less tedious to write equations in a spreadsheet than to do the arithmetic by hand.

Morning time and afternoon time are found by subtracting the start time from the end time. Then the time for the day is found by adding the morning and afternoon shift hours.

Rounding to the nearest quarter hour can be done a couple of ways. In a spreadsheet, you multiply hours by 4, round to an integer, then divide that integer by 4 to get the rounded hours. (In a spreadsheet, hours are 1/24 of a day. When the hours:minutes are converted to decimal, you get a number of days. To make hours again, you need to multiply that by 24.)

Of course, hours are multiplied by $12.50 to get pay for all days but Sunday. For Sunday, that product is again multiplied by 1.5 for "time and a half."

The total pay is $392.19.

Suppose that you take 300 mg of an antibiotic every 6 hr. The half-life of the drug is 6 hr (the time it takes for half of the drug to be eliminated from your blood). Use infinite series to find the long-term (steady state) amount of antibiotic in your blood exactly.

Answers

Answer:

1200000

Step-by-step explanation:

Esun as ma

Negative 6 equal 2/9 x

Answers

Step-by-step explanation:

-6 = 2/9 x

2/9x = -6

x = (-6)×9/2

= -27

Question 1
Elena, Lin, and Noah all found the area of Triangle Q to be 14 square units but
reasoned about it differently, as shown in the diagrams. Explain at least one student's
way of thinking and why his or her answer is correct.
Q
Lin
Elena
Q
Noah

Answers

Answer:

For Lin's answer

Step-by-step explanation:

When you have a triangle, you can flip it along a side and join that side with the original triangle, so in this case the triangle has been flipped along the longest side and that longest side is now common in both triangles. Now since these are the same triangle the area remains the same.

Now the two triangles form a quadrilateral, which we can prove is a parallelogram by finding out that the opposite sides of the parallelogram are equal since the two triangles are the same(congruent), and they are also parallel as the alternate interior angles of quadrilateral are the same. So the quadrilaral is a paralllelogram, therefore the area of a parallelogram is bh which id 7 * 4 = 7*2=28 sq units.

Since we already established that the triangles in the parallelogram are the same, therefore their areas are also the same, and that the area of the parallelogram is 28 sq units, we can say that A(Q)+A(Q)=28 sq units, therefore 2A(Q)=28 sq units, therefore A(Q)=14 sq units, where A(Q), is the area of triangle Q.

The reason is while computing the area is found to be 14 square units.

What is area of triangle?

The area of Triangle = 1/2* base *  height

given:

assumed area to be 14 square units

We will take the case of Elena

In figure the base = 7 units

height = 4 units

Area of triangle

=1/2*base*height

=1/2 * 7 * 4

=7*2

=14 square units

Learn more about area of triangle here:

https://brainly.com/question/22359772

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At the PNE. On Friday night 2,950 people attended the monster truck show. On Saturday night, 3,159 people attended. In the stadium seats 4,000 people, how many empty seats were there for the two nights?

Please show how u get the answer!
Help fast

Answers

Answer:

1891 empty seats.

Step-by-step explanation:

for night 1: 4000- 3159= 841.

for night 2: 4000- 2950= 1050.

1050+841= 1891.

there were 1891 empty seats for the two nights.

I will mark as BRANLIEST!!!

How would you begin to answer this question- solve for x if, 2x + 3x = 10. what’s the answer? Plz help me! I’m desperate

Answers

First you add like terms, so in this case it would be 2x+3x, which would together make 5x=10. Then to get x isolated divide 10 by 5 and x=2

Answer:

You would begin to start this equation by combining like terms.

Step-by-step explanation:

To start you would first combine 2x + 3x and you get 5x. From there you would solve 5x=10. Now you would divide by 5 on both sides to get x=2.

i’m bad at math. this is right?

Answers

Answer: B

Step-by-step explanation:

The converse means X --> Y , so Y --> X.

In other terms, you just need to reverse the terms and review that it turns out correct. In answer B, it does that just right.

Answer:

It should be the second one.

Step-by-step explanation:

Converse is just switching the hypothesis and conclusion, or the "if... then..." portion of the conditional.

To simplify an expression means to ensure there are no parentheses and no like
terms.
True
Or
False

Answers

Answer:

True, there you go! hope it helps! Please vote Brainliest!

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

To simplify an expression means to ensure there are no parentheses and no like terms.

1. IV+61-6=6
Solving absolute value?

Answers

Answer:

[tex]\frac{ -49i − 49v }{iv}[/tex]

Step-by-step explanation:

v= −49

i= −49

A physical therapy facility is building a new pool that is 60 feet long and 7 feet deep. They have ordered enough tile for a
140-foot-long border around the edge. How wide should the pool be to ensure that all tiles are used?

Answers

Answer:

The Pool should be 10 feet wider

Step-by-step explanation:

The rectangngle shaped pool will have 4 sides...

If the Pool is 60 feet long then 120 feet should be covered by Tiles.

so only Tiles of 20 feet are left...

Hence the border will be 10 on one side and 10 on the other side

The Pool should be 10 feet wider

The calculation is as follows:

The rectangle-shaped pool will have 4 sides

In the case when the Pool is 60 feet long then 120 feet should be covered by Tiles.

Thus,  only Tiles of 20 feet are left...

Therefore,  

Hence the border will be 10 on one side and 10 on the other side

Learn more: https://brainly.com/question/17429689?referrer=searchResults

7. A BOOKSTORE WAS SELLING BOOKS FOR 50% OFF. A SHELF IN THE STORE HAD A SIGN AS SHOWN:
"BOOKS ON THIS SHELF TAKE AN ADDITIONAL 25% OFF"
LETA PICKED OUT BOOKS FROM THE DISCOUNT SHELF THAT HAD A REGULAR PRICE OF $100. HOW MUCH
DID LETA PAY FOR THE DISCOUNTED BOOKS?

Answers

Answer:

Leta payed $37.50

Step-by-step explanation:

50% is another way of saying half. So half of 100 is 50. She is down to $50.00 If you take another 25% off then it is $37.50. This is because 25% of 50 is 12.50. If you subtract 12.5 from 50 then you get 37.50. This is how I know it is $37.50. Hope this helps! :)

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