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]


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Solve using the method of your choice:
[tex]2 {x}^{2} + 3x - 2 = 0[/tex]

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Answer:

x=½, -2

x= 0.5, -2

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How do I solve this?

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Step-by-step explanation:

Slope= -3/1

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Step-by-step explanation:

Just so that we have something to work with, the length of the longest day (June 22) in Acron Ohio is 15 hours 8 minutes and 9 seconds on the 20th of June of this year. The number we get won't be this accurate, but it will tell us if we have done it correctly. The tricky part is when to use the radians.

cos(0.1309 H) = -0.4336 tan (40o 46 minutes)  I have assumed this is in radians. It won't work any other way. The measurement cannot be in degrees which will give a negative tan from the minus sign out in front. The cos being minus will make things even worse.

cos(0.1309 H) = -0.4336 tan (40 46/60  )

cos(0.1309 H) = -0.4336 tan (40.766666667)

cos(0.1309 H) = -0.4336 * -0.074173405

cos(0.1309 H) = 0.032161588

0.1309 H = cos-1(0.032161588)

0.1309 H =  1.538629191

H = 1.538629191 / 0.1309

H = 11.754 which is no where near 15 hours, but it is what the numbers give.

I would suggest that you go to your instructor for the other two. Work this one out until you get somewhere near 11.7 hours.

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The product of the number g and the opposite of 7 is equal to k.
Change to an algebraic expression

Answers

answer: -7g = k

explanation: -7 is the opposite of 7
g(-7) = k. Hope this helps. You don’t need brackets by the way you can just say -7g or g times -7 if you want. Hope this helps and a Brainliest would be appreciated

pls help will give brainliest

Answers

Answer:3rd one

Step-by-step explanation:

If p = 5, q = 4, and r = 1, what is the value of p - r ?

a. 3
b. 4
c. 6
d. 1

Answers

The answer is 4

We can replace p with 5 and r with 1, this will lead us with 5 - 1.
b. 4

If p=5 and R= 1 then 5-1=4

Which values of a, b, and c correctly represent the answer in simplest form?

4 and one-half divided by 1 and one-fourth = a StartFraction b Over c EndFraction
a = 3, b = 6, c = 10
a = 3, b = 3, c = 5
a = 5, b = 3, c = 3
a = 10, b = 6, c = 3

Answers

Answer

the answer is a i

thinnk

Step-by-step explanation:

hope this helped!!

The values of the fraction are a = 3, b= 3,   c= 5 is the correct answer.

What is a fraction?

A fraction is a part of a whole number, and a way to split up a number into equal parts. It is a number expressed as a quotient, in which a numerator is divided by a denominator.

For the given situation,

The fraction is given as  [tex]\frac{4\frac{1}{2} }{1\frac{1}{4} }[/tex]

⇒ [tex]\frac{\frac{9}{2} }{\frac{5}{4} }[/tex]

⇒ [tex]\frac{9}{2}[/tex] × [tex]\frac{4}{5}[/tex]  

⇒ [tex]\frac{18}{5}[/tex]

⇒ [tex]3\frac{3}{5}[/tex]

Thus from the above value a = 3, b= 3, c= 5.

Hence we can conclude that the values of the fraction are a = 3, b= 3,   c= 5 is the correct answer.

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What is 40 percent of 50?
1. 20
2. 30
3. 40
4. 10

Answers

Answer:

1) 20

Step-by-step explanation:

40% percent of this number is only a small amount.

20

Step-by-step explanation:

40 percent of this number is a small amount

Simplify. 32v2 the power of 4/ 8v to the power of 6

Answers

the answer is 4/v to the power of two

Mike invests $12,500 at 9% for a term of 12 years. What is the interest earned for his investment?

Answers

Answer:

$13.5

Step-by-step explanation:

l= P×R×T/100

I= 12,500×9×12/100

l= $13,5

The interest earned for his investment after 12 years is $13,500.

What is the simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, P=$12,500, rate of interest=9% and time period=12 years.

Here, simple interest = (12500×9×12)/100

= 1350000/100

= 13,500

So, the interest is $13,500

Therefore, the interest earned for his investment after 12 years is $13,500.

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determine the range of the following graph:

Answers

Answer:

(-15)

Step-by-step explanation:

(-7) - 8 = (-15) (Range is the difference between Max and Min Value)

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Find the values of x and y.

x=

Answers

x = 40°
y = 6

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Your brother asked you to help him build a bookcase for your next-door neighbor. Since he is doing most of the work, you get 3 dollars for every 5 dollars he makes. He got paid 67 dollars. How much did you get paid?

Answers

Answer:

So, friend Let me solve the question for you :

let's use disturbutive property

67 x 5 - 67 × 3

67 × (5-3)

67 ×2 = 134

Step-by-step explanation:

Hope it. helps PISas Markbrainliest

Answer:

You got paid $40.20

Step-by-step explanation:

First let's find out how many 5's they gave him:

$67 (brother's money) ÷ 5 = 13.4 (how many times they paid him)

Now we find out how much money they gave you:

$3 (how much they give you) x 13.4 = $40.20 (your total money)

when writing fraction from a graph does the x axis number go on top or bottom​

Answers

Answer:

x ax-s can be horizontal and top

y axis is bottom

Step-by-step explanation:

1 Later that afternoon, Robert spent more time playing the video game.
He earned 88 points. How many points did he tell his friend that
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Answers

This doesn’t seem like the full question...
Do you have a picture so I can answer it lol

If A is the least common multiple of 12, 24, and 36, and B
is the lowest prime number, what is the sum of A and B ?

F.
3
G.
4
H.
73
J.
74
K.
145

Answers

Answer:

74

Step-by-step explanation:

A= Least common multiple of 12,24,36

Factors of 12 = 2*2*3

Factors of 24 = 2*2*2*3

Factors of 36 = 2*2*3*3

A = 2*2*2*3*3 = 72

B = Lowest prime number = 2

A+B = 72+2 = 74

Explain how sample size affects statistical significance.

Answers

Answer:

More formally, statistical power is the probability of finding a statistically significant result, given that there really is a difference (or effect) in the population. ... So, larger sample sizes give more reliable results with greater precision and power, but they also cost more time and money.

What is 86.929 rounded to the nearest tenth ?

Answers

Answer:

86.9

Step-by-step explanation:

This is because after the decimal point, it goes to the tenths place and then the thousands place, therefore, if you round it, it would be 86.9.

Please Assist!
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Answers

Answer:

[tex](-5,\frac{1}{2} )[/tex]

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]

Simply plug in your coordinates into the midpoint formula to find midpoint:

R(-2, 3)

S(-8, -2)

[tex](\frac{-2+-8}{2},\frac{3+-2}{2} )[/tex]

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Answers

Answer:

AB is 13

Step-by-step explanation

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Answers

Complete question :

Find the standard deviation of the following data. Round your answer to one decimal place.

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Answer:

1.833

Step-by-step explanation:

Given the data :

X: 0 1 2 3 4 5

P(X) : 0.2, 0.3, 0.1, 0.1, 0.1, 0.2

Standard deviation (s) = Sqrt[Σx²*f(x) - E(x)²]

E(x) = (0*0.2) + (1*0.3)+(2*0.1)+(3*0.1) + (4*0.1) + (5 * 0.2) = 2.2

Sqrt[Σx²*f(x) - E(x)²]: [(0^2 * 0.2)+(1^2 * 0.3)+(2^2 * 0.1)+(3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.2)] - 2.2²

Sqrt(8.2 - 4.84) = 1.833

I NEED HELP HERE ASAP, I’m giving brainliest to the right one. I forgot how to solve this:/

Answers

Answer:

28 weeks

Step-by-step explanation:

It says that $42 was 1/3 of her total. So you multiply $42 by 3 and you get $126. You now divide $126 by her weekly allowance, $4.5, and the answer is 28.

1. $42 x 3 = $126

2. $126/$4.5 = 28

3. The answer is Sharon has been saving her allowance for 28 weeks.

Hope this helps!

-Jerc

Answer:

She has been saving her money up for 28 weeks.

Step-by-step explanation:

1. If 42 is 1/3 of her money, then you would multiply 42 by 3 to get the full 3/3 so: 423=126

2. Next, you would divide $126 by $4.50 because that is the total amount of money divided by how much she saved up each week, so: 126/4.5=28 and that gives us the answer which is 28.

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Answers

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is this the question ?

Step-by-step explanation:

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Answers

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Answers

I think it’s but I’m not sure E

Answer:

:)

Step-by-step explanation:

The product of 3 consecutive integers is 4,896. What is the largest of the three consecutive numbers?

Answers

Answer:

18

Step-by-step explanation:

1. Try to create an equation. We can say that the first number is x and the following numbers are x+1 and x+2. That means that x*(x+1)*(x+2)=4896.

2. Solve and Simplify. x^3+3x^2+2x=4896.

3. Solve and Simplify (2) I'm assuming that you're not looking for the complex solutions, so x=16.

4. Find the 3rd number. 16+2=18

Answer: 18 is the largest number of the three

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Answer:

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Step-by-step explanation:

Answer:

4

Step-by-step explanation:

40+14=54 and 50 = 4 + 54

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Round 1.24236 to the nearest hundredth

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Answer:

1.24

Step-by-step explanation:

Thomas wants to put a fence around a rectangular garden that is 12 feet long and 7 feet wide. How much fencing will he need?

Answers

Answer:

he need 84

Step-by-step explanation:

12* 7

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Answer:

38 feet

Step-by-step explanation:

Find the perimeter:

12 + 7 + 12 + 7 = 24 + 14 = 38 feet of fencing

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