Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,100, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $13 for each 4-cylinder connecting rod and $16 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let

x4 = the number of 4-cylinder connecting rods produced next week
x6 = the number of 6-cylinder connecting rods produced next week
s4 = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
s6 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

Required:
Using the decision variables x4 and s4, write a constraint that sets next week.

Answers

Answer 1

Answer:

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     [tex]x_4 \le W_4 *  s_4[/tex]

    [tex]x_4 \le 5000 *  s_4[/tex]

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     [tex]x_6 \le W_6 *  s_6[/tex]

     [tex]x_6 \le 8,000 *  s_6[/tex]

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     [tex]x_4 \le W_4 *  s_6[/tex]

=>   [tex]x_4 \le 5000 *  s_6[/tex]

     [tex]x_4 \le W_6 *  s_4[/tex]

=>    [tex]x_4 \le 8000 *  s_4[/tex]

     [tex]s_4 + s_6 = 1[/tex]

The minimum cost of production for next week is  

   [tex]U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6[/tex]

=>  [tex]U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6[/tex]

Step-by-step explanation:

The cost for the four cylinder production line is  [tex]C_4 =  \$2,100[/tex]

The cost for the six cylinder production line is  [tex]C_6 = \$3,500[/tex]

The manufacturing cost for each four cylinder is  [tex]M_4= \$13[/tex]

 The manufacturing cost for each six cylinder is [tex]M_6= \$16[/tex]

  The weekly production capacity for 4 cylinder connecting rod is [tex]W_4 = 5,000[/tex]

   The weekly production capacity for 6 cylinder connecting rod is [tex]W_6 = 8,000[/tex]

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     [tex]x_4 \le W_4 *  s_4[/tex]

    [tex]x_4 \le 5000 *  s_4[/tex]

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     [tex]x_6 \le W_6 *  s_6[/tex]

     [tex]x_6 \le 8,000 *  s_6[/tex]

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     [tex]x_4 \le W_4 *  s_6[/tex]

=>   [tex]x_4 \le 5000 *  s_6[/tex]

     [tex]x_4 \le W_6 *  s_4[/tex]

=>    [tex]x_4 \le 8000 *  s_4[/tex]

     [tex]s_4 + s_6 = 1[/tex]

The minimum cost of production for next week is  

   [tex]U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6[/tex]

=>  [tex]U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6[/tex]


Related Questions

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Answers

Answer:

y= (5/2)x+2

Step-by-step explanation:

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The slope of AB is 6/5 if point A is (3,y) and point B is (-2,-1) find the value of y

Answers

If we put these informations in the problem into the equation of slope,

6/5 = y+1 / 2+3

To find y,

y+1 = 6

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Answer:

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Answer:

y=4x+11

Step-by-step explanation:

y=mx+b.          

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Answer:

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Step-by-step explanation:

what is the quotient of
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Answer:The exact form is -10/7  the simplified form is -1 3/7

Step-by-step explanation:

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12b+72 is the answer
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Shonda painted 3 walls in her home. She used 34 of her paint. She used the same amount of paint on each wall.

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Drag and drop the correct answer to complete the statement.

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Please help me

Answers

Answer:

en que exactamente necesitas mi ayuda????

Step-by-step explanation:

???????

Answer: Shonda used 1/4 of her paint on each wall.

Step-by-step explanation:

If she used 3/4 of her paint on 3 walls, then each wall used up 1/4 of her paint.

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Hope this helps!

The original price for a jacket is $124.95. It is on sale for 20% off. Which of the following gives the best estimate of the savings?

Answers

Answer:

24.99

Step-by-step explanation:

We first must figure out the current price of the jacket, we need to multiply the original price (124.95) times .80 (1.00 - .20). Doing so we get a total of 99.96. In order to find the savings, we subtract the original price by the new price. 124.95-99.96 = a savings of 24.99

Answer:

You would be saving 24.99 dollars

Step-by-step explanation:

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Hope this helps!

5x-(x+3)=1/3(9x+18)-5

Answers

Answer: x=4

Step-by-step explanation:

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Do u have a picture I’d the graph?

What is the product of-3 and-13? Enter your answer as a mixed number, in simplified fom, in the box​

Answers

Answer:

39

Step-by-step explanation:

-3x(-13) = 39.

If this question was asking for something different I apologize.

Piper and her children went into a movie theater and she bought $59.50
bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs
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Answers

6 candy boxes

Step-by-step explanation :

Since they both bought their own popcorn that means they both spent $8 on popcorn making that a total of $16. Therefore we now only need to find one variable which is the number of candy boxes that they bought in order to reach the $25 total that they spent. This variable can be represented as x in the following algebraic equation.

(2*8) + 1.50x = 25

16 + 1.50x = 25 ... subtract 16 from both sides

1.50x = 9 ... divide both sides by 1.50

x = 6

Finally, we can see that Billy and Tommy bought a total of 6 candy boxes.

Answer:

This is the answer on Delta Math

Step-by-step explanation:

Type the correct answer in each box. Use numerals instead of words. For this question, any answer that is not a whole number should be entered as a fraction in simplest form, using / as the fraction bar, or as a decimal number rounded to the hundredths place. The point P has a value of and is represented with a point on the top number line. The point R has a value of and is represented with a point on the bottom number line. If the value of point P is and |Q| is , then the greatest value of P + Q is , and the least value of P + Q is . If the value of point R is and |S| is 2, then the greatest value of R + S is , and the least value of R + S is . Reset Submit

Answers

Answer:

Step-by-step explanation:

Since we are not given the value of P, |Q|, R and S, we can as well assume values for them for the sake of this question.

Let P = 5, |Q| = 6, R =7 |S| = 2

Note that since Q and S are in modulus sign, they can return both positive and negative values.

P+Q = 5 + 6 (note that the positive value of Q is used since we need the greatest value of P+Q)

P+Q = 11

Hence the greatest value of P+Q is 11

For the least value of P+Q, we will use the negative value of Q as shown

P+Q = 5+(-6)

P+Q = 5-6

P+Q = -1

Hence the least value of P+Q is -1

Similarly:

R+S = 7 + 2 (note that the positive value of S is used since we need the greatest value of R+S)

R+S = 9

Hence the greatest value of R+S is 9

For the least value of R+S, we will use the negative value of S as shown

R+S = 5+(-2)

R+S = 5-3

R+S = 2

Hence the least value of P+Q is 2

NOTE THAT THIS ARE ASSUMED VALUES. ALL YOU NEED IS TO PLUG IN THE VALUES OF P, Q and R THAT YOU HAVE IN CASE THE VALUES DIFFERS.

The standard height from the floor to the bull’s-eye at which a standard dartboard is hung at 5 feet 8 inches. A standard dartboard is 18 inches in diameter. Suppose a standard dartboard is hung at standard height so that the bull’s-eye is 10 feet from the wall to its left. Sasha throws a dart at the dartboard that land at point 10.25 Feet from the left wall and 5 feet above the floor. Does Sasha’s dart land on the dartboard? Drag the choices into the boxes to correctly complete the statements.

Answers

Answer:

Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!

The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.  

The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.

This quiz was completed on k12, lesson 3.03.

The question is an illustration of equation of circles.

The equation of the dartboard circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]Sasha's dart lands on the dartboard because

From the question, we understand that:

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex] ---- the height at which the dartboard was hung

[tex]\mathbf{d = 18\i n }[/tex] ---- the diameter of the dartboard

[tex]\mathbf{B = 10ft}[/tex]  --- the bull's eye

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] --- Sasha's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }[/tex]

Take LCM

[tex]\mathbf{h = \frac{15 + 2}{3}\ ft }[/tex]

[tex]\mathbf{h = \frac{17}{3}\ ft }[/tex]

[tex]\mathbf{d = 18\i n }[/tex]

[tex]\mathbf{d = \frac{18}{12}ft}[/tex]

[tex]\mathbf{d = \frac{3}{2}ft}[/tex]

Divide by 2 to calculate radius

[tex]\mathbf{r = \frac{3}{2*2}ft}[/tex]

[tex]\mathbf{r = \frac{3}{4}ft}[/tex]

The equation of the circle is represented as:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]

In this case:

[tex]\mathbf{a = B = 10ft}[/tex] -- the distance between the bull's eye and the wall

[tex]\mathbf{b = h = \frac{17}{3}\ ft }[/tex] ---- the height at which the dartboard was hung

So, we have:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}[/tex]

Evaluate the exponents

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Hence, the equation of the circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Does Sasha’s dart land on the dartboard?

Yes her dart lands on the dartboard because

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] is within the circumference of the dartboard

Read more about equation of circles at:

https://brainly.com/question/23988015

What is 4 1/4 ÷ 4 1/2

Answers

Answer:

Your answer is going to be 17/18.

Step-by-step explanation:

You are going to put the fractions in improper form, giving you 17/4 and 9/2. Then you are going to use the saying KCF Keep Change Flip.

(17/4)(2/9)

34/36

17/18

Determine whether y^2=−3x−2 is a function.

Answers

Answer:

y=3x-2 is a function because it passes the vertical line test.

Step-by-step explanation:

The given equation y² = - 3x - 2 represents a function.

What is a function?

A function is  the relation between two sets. The first one is called domain and the second one is called range.

Given, y² = - 3x - 2

For x = 0, y = √(- 3 × 0 - 2) = √(-2)

For x = 1, y = √(- 3 × 1 - 2) = √(-5)

For x = -1, y = √[- 3 × (- 1) - 2) = ± 1

For any value of 'x' in the domain, 'y' has at least a value in the range.

Hence, the given equation represents a function.

Learn more about a function here: brainly.com/question/3951330

#SPJ3

What is the probability that you will get heads no more than once out of 3 flips? P(0 successes) + P(1 success)=

Answers

Answer:

The answer is .5

Step-by-step explanation:

Answer:

The correct answer is 0.5

Step-by-step explanation:

You have to do 0.125 (0 successes) plus 0.375 (1 success). This is equal to 1/2

This is correct on edge.

Which expression has the same value as -18÷(-9)?

A-18-2

B-12÷(-3)

C-10÷5

D-6÷(-4)​

Answers

Answer:

None of the following

Step-by-step explanation:

-18 ÷ (-9) = 18 ÷ 9 = 2

A. -18 - 2 = -(18 + 2) = -20 ≠ 2

B. -12 ÷ (-3) = 12 ÷ 3 = 4 ≠ 2

C. -10 ÷ 5 = - 2 ≠ 2

D. -6 ÷ (-4) = 6 ÷ 4 = 1.5 ≠ 2

The price for a new car, without sales tax, is
$18,900. The buyer must also pay a 5% state
sales tax. What is the cost of the car includ-
ing the sales tax?

Answers

Answer:

Step-by-step explanation:

18900 divided by 10 = 1890

1890 divided by 2 is 945

945 is 5 percent of 18900

18900 + 945 = 17955

Answer = 19845

Answer : $19,845

5% of 18,900
= 945

The price for the car
= $18,900

$18,900 + 5
= $19,845

6m + 4n + 3m - 6

What are the terms? Separate them with a comma.

Answers

6m, +4n, +3m, -6

(I also added a picture)

five times the sum of a number and four

Answers

here is the Answer:

5(x+4)

Hope it helps

how math is used in technology

Answers

Answer:read the explanation

Step-by-step explanation:

The processors that power computers are able to perform calculations quickly, and the calculations are performed using Boolean algebra. People generally solve math problems using a base-10 number system. Boolean algebra relies on base-2 math, in which all numbers are represented using ones and zeros.

In addition to calculating basic math problems, however, computers also use Boolean logic. This logic, which is rooted in discrete mathematical principles, allows computers to solve problems that require making logical decisions. Boolean algebra and logic combine to make sophisticated devices; self-driving cars, for example, use the input calculated from digital cameras to make decisions about how to navigate.

8) There are 6 cups of sugar in 5 batches of cookies. How many cups are in 1 poin
1 batch?

Answers

Answer:

6/5 cups

Step-by-step explanation:

[tex]6 \:cups = 5\:batches\\x\:cups = 1\:batch\\\\Cross\:Multiply\\\\5x = 6\\\\Divide\:both\:sides\:of\:the\:equation\:by\:5\\\\\frac{5x}{5} =\frac{6}{5} \\\\x = 1\frac{1}{5}[/tex]

Sharon buys a 60" tv for $1,450 plus the sales tax rate, which is 8.25%. what is the total cost of what she paid after taxes. round to two decimal place ​

Answers

Answer:

1,569.625

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total cost of the 60" TV is $1,569.63.

Write the following equation in the general form Ax+ By+ C:
1/2y -1/3x -1 = 0
a.) -2x +3y -6 = 0
b.) 2x -3y -6 = 0
c.) 2x 3y +6 = 0


Answers

C the answer hehehehehehehwhw

If f(x) = 2x - 3, find f(-2).

Answers

Answer:

f(-2) is -7

Step-by-step explanation:

input -2 as x

2(-2)-3

-4-4

-7

Question 2 of 5

Select the story problem that this division problem represents.

3

4

1

5

A. A mosaic has an area of square foot and a width of foot.

What is the length of the mosaic?

B. A piece of wrapping paper is yard wide and yard long. What is

the area of the wrapping paper?

C. The area of a wetland is į square mile, and it is mile in length.

How wide is the wetland?

D. A whiteboard is meter long and has an area of 1 square meter.

How wide is the whiteboard?

Answers

Answer:

The answer is below

Step-by-step explanation:

A) Given that the area of the square a square foot = 1 ft², the width = 1 foot

Area = length × width

1 ft² = length × 1 ft

Length = 1 ft²/ 1 ft = 1 ft

B) Given that length of wrapping paper = 1 yd, width = 1 yd.

The area of the paper = length × width = 1 yd × 1 yd = 1 yd²

C) Given that the area of the wetland is a square mile = 1 mile², the length = 1 mile

Area = length × width

1 mile² = 1 mile × width

width = 1 mile²/ 1 mile = 1 mile

D) Given that the area of the square a square meter = 1 m², the length = 1 meter

Area = length × width

1 m² = 1 m × width

width = 1 m²/ 1 m = 1 m

Robin Hartman earns $600 per week plus 3% of sales over $6,500. Robin's week sales are $14,000. How much does Robin earn

Answers

Answer:

$825

Step-by-step explanation:

Given that :

Weekly earning = $600 plus 3% of sales over $6500

If weekly sales = $14000

How much will Robin earn

Robin's earning will be:

Flat weekly pay + 3% of amount over 6500

$600 + 3%(weekly sales - 6500)

$600 + 0.03(14000 - 6500)

$600 + 0.03(7500)

$600 + $225

= $825

A sphere has a diameter of 8cm. Which statements about the sphere are true? Check all that apply.
• the sphere has a radius of 4cm.
• the sphere has a radius of 16 cm.
• The diameter’s length is twice the length of the radius.
• The radius’s length is twice the length of the diameter.
• The volume of the sphere 2048/3 pi. cm. cubed
• the volume of the sphere is 256/3 pi. cm. cubed

Answers

Answer:

The sphere has a radius of 4 cm.The diameter’s length is twice the length of the radius.The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.

Step-by-step explanation:

Answer:

1. The sphere has a radius of 4 cm.

3. The diameter length is twice the length of the radius.

6. The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.

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