1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
s344n2d4d5 [400]
3 years ago
9

A product can be made in sizes huge, average and tiny which yield a net unit profit of $14, $10, and$5, respectively. Three cent

ers manufacture these products. The centers respectively have a capacity ofturning out 550, 750, and 275 units of the product per day, no matter what sizes are involved. The manufacturing process necessitates cooling water and each unit of huge, average, and tiny sizesproduced require 22, 16, and 9 gallons of water, respectively. Center 1 has 11,000 gallons of coolingwater available per day, Center 2, 7000, and Center 3, 4000 gallons. The daily demand is of 710, 900,and 350 units of the huge, average, and tiny siz. By company policy, the fraction (scheduled production)(center's capacity) must be the same at all the centers. The company wishes to maximize its profits.
Required:
Model this problem as a linear program
Mathematics
1 answer:
navik [9.2K]3 years ago
6 0

Answer:

The model is:

z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃    to maximize

Subject to:

First center               X₁₁  +  X₂₁  + X₃₁  ≤  550

Second center         X₁₂  +  X₂₂  + X₃₂  ≤ 750

Third center               X₁₃  + X₂₃  + X₃₃  ≤ 275                  

22* X₁₁  + 16* X₂₁  + 9*X₃₁     ≤   11000

22* X₁₂  + 16* X₂₂  + 9*X₃₂   ≤   2700

22*X₁₃  + 16* X₂₃  +  9*X₃₃  ≤  3400

X₁₁  +  X₁₂  + X₁₃  ≤  710

X₂₁  + X₂₂ + X₂₃  ≤  900

X₃₁ + X₃₂ + X₃₃  ≤  350

2700*(X₁₁  +  X ₂₁  + X₃₁)  -  11000*(X₁₂ + X₂₂ + X₃₂) = 0

3400*(X₁₁  +  X ₂₁  + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0

Xij >= 0

Step-by-step explanation:

Let´s call Xij   product size i produced in center j

According to this, we get the following set of variable

X₁₁    product size huge produced in center 1

X₁₂    product size huge produced in center 2

X₁₃   product size huge produced in center 3

X₂₁   product size average produced in center 1

X₂₂   product size average produced in center 2

X₂₃   product size average produced in center 3

X₃₁  product size-tiny produced in center 1

X₃₂ product size-tiny produced in center 2

X₃₃ product size-tiny produced in center 3

Then Objective function is

z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃

Constrains

Center capacity

1.-   First center               X₁₁  +  X₂₁  + X₃₁  ≤  550

2.-   Second center         X₁₂  +  X₂₂  + X₃₂  ≤ 750

3.- Third center               X₁₃  + X₂₃  + X₃₃  ≤ 275

Water available

1.-  22* X₁₁  + 16* X₂₁  + 9*X₃₁     ≤   11000

2.-  22* X₁₂  + 16* X₂₂  + 9*X₃₂   ≤   2700

3.-   22*X₁₃  + 16* X₂₃  +  9*X₃₃  ≤  3400

Demand constrain

Product huge

X₁₁  +  X₁₂  + X₁₃  ≤  710

Product average

X₂₁  + X₂₂ + X₂₃  ≤  900

Product tiny

X₃₁ + X₃₂ + X₃₃  ≤  350

Fraction SP/CC must be the same

First and second centers  fraction SP/CC  

(X₁₁  +  X ₂₁  + X₃₁)/ 11000   =  (X₁₂ + X₂₂ + X₃₂)/ 2700

2700*(X₁₁  +  X ₂₁  + X₃₁)  -  11000*(X₁₂ + X₂₂ + X₃₂) = 0

First and third centers  fraction SP/CC  

(X₁₁  +  X ₂₁  + X₃₁)/ 11000   = ( X₁₃ + X₂₃ + X₃₃)/ 3400

3400*(X₁₁  +  X ₂₁  + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0

The model is:

z = 14* X₁₁ + 14*X₁₂ + 5*X₁₃ + 10*X₂₁ + 10*X₂₂ + 10*X₂₃ + 5*X₃₁ + 5*X₃₂ + 5*X₃₃

Subject to:

First center               X₁₁  +  X₂₁  + X₃₁  ≤  550

Second center         X₁₂  +  X₂₂  + X₃₂  ≤ 750

Third center               X₁₃  + X₂₃  + X₃₃  ≤ 275                  

22* X₁₁  + 16* X₂₁  + 9*X₃₁     ≤   11000

22* X₁₂  + 16* X₂₂  + 9*X₃₂   ≤   2700

22*X₁₃  + 16* X₂₃  +  9*X₃₃  ≤  3400

X₁₁  +  X₁₂  + X₁₃  ≤  710

X₂₁  + X₂₂ + X₂₃  ≤  900

X₃₁ + X₃₂ + X₃₃  ≤  350

2700*(X₁₁  +  X ₂₁  + X₃₁)  -  11000*(X₁₂ + X₂₂ + X₃₂) = 0

3400*(X₁₁  +  X ₂₁  + X₃₁) - 11000*( ( X₁₃ + X₂₃ + X₃₃) = 0

Xij >= 0

You might be interested in
A fish aquarium that needs water measures 5ft long by 3 feet wide by 2 feet tall. If Josh only has has 12ft of water, how much m
Pepsi [2]

Answer:

Step-by-step explanation:

18 ft

6 0
3 years ago
Read 2 more answers
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y.
wolverine [178]

Answer:

\lambda=10^{-10}\ m

Step-by-step explanation:

Given that,

The frequency of x-rays, f=3\times 10^{18}\ Hz

We need to find the wavelength for x-rays. The relation between wavelength, frequency and speed of light is given by :

v=f\lambda\\\\\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^{8}}{3\times 10^{18}}\\\\=10^{-10}\ m

So, the wavelength for x-rays is 10^{-10}\ m.

7 0
3 years ago
Need help will mark Brainliest
Svetach [21]

Answer:

250 ft.

Step-by-step explanation:

It seems that you are learning the side-splitter theorem right now. If a line is parallel to one side of the triangle and intersects the other two sides, it divides the side proportionally. From the picture we can tell that the streets are parallel, with a line of intersection. Therefore, we can create the following equation of proportionality:

\frac{375}{300}  = \frac{x}{200}

Now that we have this equation, we can use the <u>butterfly method</u> to solve for x. We <u>cross multiply</u>:

375*200=300x\\

Now, all we have to do is <u>isolate</u> the variable to find x:

75000=300x\\x=250

Therefore, the distance of Orange Ave between the 3rd St. and 4th St. is 250 ft.

<em>I hope this helps! Please let me know if you have any further questions :)</em>

5 0
2 years ago
Which shows how to solve the equation 3/4x -6 for x in one step
Aleksandr [31]

Answer:

A

Step-by-step explanation:

You can multiply both sides on an equation by the reciprocal to cancel the fraction on the first side.

8 0
2 years ago
Problem: – 12 = - Зу
Rzqust [24]

Answer:

4y or 4 (divide)

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • you are building a fence 13ft long. on monday you build 4 1/3 feet of the fence, on tuesday 5 3/4 feet. how much do you still ne
    13·1 answer
  • Which property of inequality should you use to solve 3x ≤ 27?
    8·1 answer
  • What is X squared +3x-70
    11·1 answer
  • I will mark brainlest and give 50 points.
    5·1 answer
  • 1. The amount paid for different weights of oranges at a farmer’s market are shown below. Oranges (lb) Price ($) 2 3 3 4.50 5 7.
    11·1 answer
  • JUST LOOK AT PICTURE THANK YOUUU
    8·2 answers
  • How do I delete this
    7·1 answer
  • Ahh please help!! (•☆•)♡♡♡aa please help me like it would mean the world​
    12·2 answers
  • Evaluate a^2b^2? when a = 5 and b = 3.
    12·1 answer
  • Carly owns a toy store. She sells teddy bears and charges $25 per bear. Her total monthly cost is $3765. How many bears does Car
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!