5

Finish Furniture manufactures tables in facilities located in three cities-Reno Denver; and Pittsburgh. The tables are then shipped to three retail stores located i...

Question

Finish Furniture manufactures tables in facilities located in three cities-Reno Denver; and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland and Chicago. Management wishes to develop distribution schedule that will meet the stores demand at the lowest possible cost. The shipping cost per unit from each of the sources t0 each of the destinations is shown in the following table:TO PHOENIX CLEVELAND CHICAGOFROMRENQ DENVER PITTSBURGHS15 S12 S18S19 S13 S42T

Finish Furniture manufactures tables in facilities located in three cities-Reno Denver; and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland and Chicago. Management wishes to develop distribution schedule that will meet the stores demand at the lowest possible cost. The shipping cost per unit from each of the sources t0 each of the destinations is shown in the following table: TO PHOENIX CLEVELAND CHICAGO FROM RENQ DENVER PITTSBURGH S15 S12 S18 S19 S13 S42 The available supplies are 120 units from Reno. 200 from Denver; and [60 from Pittsburgh. Phoenix has demand of 140 units, Cleveland has demand of 160 units; and Chicago has demand of 180 units. Draw nelwork for this problem and formulate it as linear program



Answers

Manufacturing Furniture A furniture factory makes wooden
tables, chairs, and armoires. Each piece of furniture requires
three operations: cutting the wood, assembling, and finishing.
Each operation requires the number of hours given in the table.
The workers in the factory can provide 300 h of cutting, 400 h
of assembling, and 590 h of finishing each work week. How
many tables, chairs, and armoires should be produced so that
all available labor-hours are used? Or is this impossible?
$$\begin{array}{|c|c|c|c|}\hline & {\text { Table }} & {\text { Chair }} & {\text { Armoire }} \\ \hline \text { Cutting (h) } & {\frac{1}{2}} & {1} & {1} \\ {\text { Assembling (h)}} & {\frac{1}{2}} & {1 \frac{1}{2}} & {1} \\ {\text { Finishing }(\mathbf{h})} & {1} & {1 \frac{1}{2}} & {2} \\ \hline\end{array}$$

So in this manufacturing of thes office chairs, there are three models that they use a list. How much cloth still in plastic they will need. Now, if we have exactly 476 years of cloth or 140 units of still an eight 126 years of plastic, they want us to figure out the best use of these. So what we're going to do is so first, I'm gonna call Utilities X secretarial. Why? At managerial Z. So from this we can come up with a system of equations in the following way. So for how much cloth will be used in total So we can get that from this first row here. So it would be three units a cloth for every utility so that the X plus four units of loss for every secretarial, which is why and then plus two times in upper managerial, which is Z, uh, to Z. And then in total, we have 476 units of cloth. And now we're gonna use that same logic for steel. So just be two x plus five. Why plus a Z is equal to or 100 and 40 and then, lastly, for plastic, we would have six X plus or why. Plus Z is equal to 8 26 So we have this system of equations here now and now. We could go ahead and start simplifying it down. So the first thing we could do is clear our exits. So what I'm going to do is looks like if we multiply row one by negative 2/3 and then add this to road to notice that we would get negative too X. And then we add that to extend the counselor. So the way I always think about this is we want the opposite sign of whatever number we have here. So negative, too. And then we just divide by whatever number we have out here in our original equation that were wanting to get cancelled so negative to over three. That's the way I always go about thinking. For those utilities, we have three X plus for why plus to see is equal to 4 76 now the X's cancel and then four times negative 2/3 plus five should give a 7/3 why and then two times negative 2/3 plus eight should give us 20 Thurdsay and then 4 76 times negative 2/3 at that 4 40 should give us 3 68/3 Let's go ahead and get rid of this zero in this plus here. Now for the next equation. Looks like we would want to multiply by. Negative, too. So would be negative. 6/3, Which gives us negative, too. So are one plus R three. So again, the X's cancel four times negative to add that four should give us negative for So we have negative for why and then two times negative, too. Plus one would give us negative three Z and then 4 76 times negative, too. Plus 8 26 should be negative. 1 26 Let's get rid of this zero here also. Right? So this is our next set of equations, and one thing I'm going to do before we move on is let's multiply this whole role here by three. Because doing that notice, we get rid of the fractions and the numbers look a lot prettier now. So 7 20 3 68 Right now, we don't have to think it's hard for wood were trying to counsel that next one. So let's see. Do you get that to cancel? It looks like So we want the negative of a negative force actually mean to this off on the side. So we want the negative of negative for and then the number. We're multiplying that seven, they're So those cancels, we want to use 4/7. So we use 4/7 Row two, plus row three to get that negative for Whitey Council. So three X plus four y plus two z Secret of 4 76 70 wide plus seven y plus 20 z is equal to 3 68 And now that why will cancel and then 20 times for seventh plus minus three should give us 59 7 z and then 3 68 times 4/7 plus negative 1 26 should give us five 97. All right, so let's get rid of this zero here and that, plus I so that we can start back substituting. So from this, this implies. Well, if we were to multiply over by seven divide by 59. That looks like we just get Z is equal to 10. Now. We want to plug this into the previous equation, so I'll do that over here. So we have seven. Why plus 20 Z is equal to 3 68 So we're going to replace Z with 10. And so that's going to give us seven wide plus 200 is equal to 3 68 because attract 200 over that gives us why is equal to 1 68 and the divided side by seven and 1 68 Divided by seven should be 20 or and now to get our last one. So we have three X plus four y plus two Z is equal to 4 76 so plugging and why that was 24 and plugging in Z. That was 10 so that we can simplify this town. So we have three x plus, so four times 24 plus 20 that's 1 16 This is equal to 4 76 So we subtract that over. So we get 3 60 Divide that by three we get 1 23 have X is equal to 1 20 So let's actually go ahead and move this up a little bit. So what we found was X is equal to 1 20 Why is equal to 24 and Z is equal to 10. So we want to make 10 managerial, 24 secretarial and 120 utility. So these right here are our solutions. And then it would probably be better to just say 120 utility, 24 secretarial and 10 managerial because that's more of what they're asking, as opposed to X, y and Z.

We are given. With total cutting overs available for week as 300 hours, total, assembling overs are $400 and total finishing overs are 590 overs. So we can assume that extra Modoff tables, y number of chairs and their number off our Armas are being produced. Hence, we can give corresponding equations as half times X plus. Why plus a said equals toe 300. Next we're half times explores three d waited by two times y plus, is there two equals two, 400 and we have explosive three divided by two. Why plus twos? They're equals to 590 Hence begin. Give corresponding augmented metrics as off 11 300 uh, three divided by 21 400 13 divided by two to 500 90. Now we can solve this father to solve it further, we converted toe a poor diagonal matrix and upper diagonal upper triangular matrix and upper triangular matrix is the matrix. They're all the elements below. Leading Dagnall are zero and hence every find a metrics as follows that is half 11 300 0/2 0 100 and the third row. Where comes a 000 90 Now we can give corresponding the questions is half X plus y plus 30 equals toe 300 half lie equals 200 and zero equals 2 90 But zero personality is not possible. Therefore, there is no solution.

Okay, So for this one, we're talking about a furniture factory that is going to produce be producing, um, chairs, cabinets and buffets. So we're going to say X's chairs. Why is buffets was very wise. Cabinets and Z is gonna be buffets on, although you can choose any three letters you want. Um, so we know that as far as like we have cutting, assembling and finishing. So it's gonna be 0.2 per chair for cutting 0.5 for buffets, points 3.5 for cabinets, 0.3 for buffets for total of 1900 50 hours. We know for assembly, it's gonna be 0.3 x plus point for why plus 0.1 z equals 14 4090. And then last but not least, this the finishing is 0.1 x plus 0.6. Why plus 0.4 z equals 2000, 160. So what we want to do is creator matrix off of this. But I'm gonna go ahead, multiply everything by 10 so I'm gonna have to five three in 19,500 three, four one and 14,900 and then 16 and four and tooth out. 21,600 for the So what? We have whole numbers instead of decimals. So the very first thing that I really want to dio has start creating this pivot pattern. So that way I have a number and then two zeros below it. So in order to do that, I'm gonna have to multiply the top by three. So I'm gonna have six, 15 nine and then 58,500 that I'm gonna I'm gonna multiply the second one by two. So it's going to be six eight to and in 29,800. Okay, so I'm gonna keep this as a to five. Three and in 19,500 for now. So then my first, that's going to be zero and then 15 minus eight s seven nine minus two is seven and then 58 500 minus minus 29 800. There's gonna be 28,700 now. Luckily, I can provide risk by seven to get 4100 and I can eliminate thes by seven to get one each. Okay, so then the next thing I need to dio is I need Teoh. Figure out what I need. Teoh at some knucklehead, multiply this bottom row by twos. That way I can eliminate it from the original top row. So to 12. Eight and 43,200 so to minus two is zero five. So 12 minus five will be seven eight minus three would be five. And then, of course, 43 1002 100 minus 19,500 is 23 700. So I have pivoted the first one. Now I am ready to pivot the second row. So what I want to do first is I want to multiply this by five. Then that's gonna be 20,500. So for now, I'm gonna leave the second row, as is, because it's about a simple fight. Is I'm going to get for this ground. So then I'm gonna have my to five minus 50 five minus three is two. And then I have 1000 left over. So now what I also notice I can do is I can divide by two now and just to make the math a little bit easier. Lips, That's what I'm going to dio. Okay, So now what I want to do is I'm gonna eliminate what? I just did this for us changing the the Matrix before it. And now I want to multiply this by seven. And this is gonna get me 28,700. So that way I can eliminate, so it's gonna be zero 07 minus five is, too. And then, of course, now I've got 5000, which I can eliminate this down by two to give me one and 2500, and then I have one final call him to pivot. So what I want to do is I want to go and just flat out subtract thes someone. I have 1001 And then, of course, 001 So I'm gonna do the first in the 3rd 1st. So this is obviously going to create zero, and then this is going to be 2000, cause it's 2500 minus 500 and then I'm going to go ahead and pivot the 1st and 2nd, so this is going to be zero, and the 4100 minus 2500 is going to be 1600. So now I have got everything down. Toe one and I have pivoted all three columns. So what this tells me is that there's gonna be 2000 chairs, 1600 buffets and 2500. I'm sorry. Um, 1600 cabinets and 2500 buffets.

Alright problem before so order costs is 1. 60 are carrying costs 32 times x over to giving a 16 x so total inventory costs is gonna be 1 60 r plus 16 x part B order quantity times number of orders per year. Give us gives us our constraint function. Then sulfur are Plug this back in to our C and we get 10 to 400 over X plus 16 x modifying our extreme points. So we take the derivative 16 minus 10 to 400 x squared set this equal to zero get X equals 80 and then plug that back into the sea to find minimum inventory costs 256 year dollars.


Similar Solved Questions

5 answers
5.) In each of the diagrams below is a particle of charge +8.4uC moving with a velocity as shown in the diagram and whose magnitude is 45 m/s. This particle is moving through a magnetic field whose direction is given. Find the magnitude and direction of the force it experiences. AlI angles must be shown in your calculations:0=.3T Finu irccnun uf @rlt Vyj Rhr1508
5.) In each of the diagrams below is a particle of charge +8.4uC moving with a velocity as shown in the diagram and whose magnitude is 45 m/s. This particle is moving through a magnetic field whose direction is given. Find the magnitude and direction of the force it experiences. AlI angles must be s...
1 answers
Kx)zo53 [x)zo53 Jo an124 /ejhawunuia4} pul (x)zsop 5 Kx)zuis _ awunssdIsqulpd VtKEh
Kx)zo53 [x)zo53 Jo an124 /ejhawunuia4} pul (x)zsop 5 Kx)zuis _ awunssd Isqulpd Vt KEh...
5 answers
Find the Wronskian of %1 2esr and y2 e-2z Use the result to determine if the two functions are linearly independent on (~0, c)W [~2e8r 22 ]Are the functions linearly independent on3, 0)?
Find the Wronskian of %1 2esr and y2 e-2z Use the result to determine if the two functions are linearly independent on (~0, c) W [~2e8r 22 ] Are the functions linearly independent on 3, 0)?...
5 answers
Constant speed by a ISN A 5.0-kg object is pulled along horizontal surlace motes 16.0 m? done by this foree thc object orce acting at 350 above the horizontal: How much work
constant speed by a ISN A 5.0-kg object is pulled along horizontal surlace motes 16.0 m? done by this foree thc object orce acting at 350 above the horizontal: How much work...
5 answers
Arcianguur trnk thate 2148 ncuntinmnnimudlmsnalons & Ihe tanz Minettim KokeIl nI (simelty YOvr annu"nc Ua = comtm woputale Anusytn }
Arcianguur trnk thate 2148 n cuntin mnnimu dlmsnalons & Ihe tanz Minettim KokeIl nI (simelty YOvr annu"nc Ua = comtm woputale Anusytn }...
5 answers
8. Does the graph below represent function and is it one-to-one?It is not a function but it is one-to-one_ Itis not a function and it is not one-to-one_ It iS a function and it is one-to-one. It is a finction but not one-to-one.
8. Does the graph below represent function and is it one-to-one? It is not a function but it is one-to-one_ Itis not a function and it is not one-to-one_ It iS a function and it is one-to-one. It is a finction but not one-to-one....
5 answers
[-/0.58[ Points]DETAILStne tth day the Ycarhoute) Philadclonia model for the @natn daylight 80)| L(t) 17 + 2.8 sin 365 incrcasin? Philaddphia couts daylight = compare how the number Use tnis model L"() June L"E) MEbOI Need Help?De5cLuaAnd June(enum
[-/0.58[ Points] DETAILS tne tth day the Ycar houte) Philadclonia model for the @natn daylight 80)| L(t) 17 + 2.8 sin 365 incrcasin? Philaddphia couts daylight = compare how the number Use tnis model L"() June L"E) MEbOI Need Help? De5cLua And June (enum...
5 answers
(8) Find the directional derivative of f(x Y) -41' - Y inthe direction of v =(3,-4} a (-1, 21.(8) Findd the equation ofthe IAngemt plane Xz-w' -~| 4t (2,3, - I)(15) Fina the eritieal pvints of F(, "-r _ 4+S,+)" Ihcn Use Ihe Second Faniuks Test elussily euch 4$ Uocul MAXIMU Ioeul minimum sudkalle poin ( the test inconelusive, stale Ilat insteud )
(8) Find the directional derivative of f(x Y) -41' - Y inthe direction of v =(3,-4} a (-1, 21. (8) Findd the equation ofthe IAngemt plane Xz-w' -~| 4t (2,3, - I) (15) Fina the eritieal pvints of F(, "-r _ 4+S,+)" Ihcn Use Ihe Second Faniuks Test elussily euch 4$ Uocul MAXIMU Ioeu...
5 answers
Consider the graphed function Based on its end behavior; which of the following could be its equation?N) (v) =x+6x? 5XB) f(v) = -1" + 6x3 54?C) f(v) = X' + 6x3 542D) f(v =-13 _ 642 54
Consider the graphed function Based on its end behavior; which of the following could be its equation? N) (v) =x+6x? 5X B) f(v) = -1" + 6x3 54? C) f(v) = X' + 6x3 542 D) f(v =-13 _ 642 54...
5 answers
Which of the following functions do not form a set of fundamental solutions of v" 4v =Select one:a. {ezt_ ~e-21,e -2t ~e2'}b {ezt_ +e-2t ,021 -e-2t}C {e2t, '021 +e-2'}d{e -21,e2'}
Which of the following functions do not form a set of fundamental solutions of v" 4v = Select one: a. {ezt_ ~e-21,e -2t ~e2'} b {ezt_ +e-2t ,021 -e-2t} C {e2t, '021 +e-2'} d {e -21,e2'}...
5 answers
Variable-density plates Find the coordinates of the center of mass of the following plane regions with variable density. Describe the distribution of mass in the region.The triangular plate in the first quadrant bounded by $x+y=4$ with $ ho(x, y)=1+x+y$
Variable-density plates Find the coordinates of the center of mass of the following plane regions with variable density. Describe the distribution of mass in the region. The triangular plate in the first quadrant bounded by $x+y=4$ with $\rho(x, y)=1+x+y$...
5 answers
Simplify. See Examples 3 and 4.$$ rac{x^{-2}}{x+3 x^{-1}}$$
Simplify. See Examples 3 and 4. $$ \frac{x^{-2}}{x+3 x^{-1}} $$...
5 answers
RchllonehrMlok TalALallon GumJor % (r)ad /o lor , [0) )Knlen Fmrelationshlp oret DracIAntIcorrtant +4 Ure EctatushscnWneed"nleysndSlnce tnocerrauLit4yletiGulitecostd, suk mt echanged betoen Iht Loo tanks Mtcin datru Aere Ltaetoltsoltu Ilc Inauivulus Eoblem 0 imAmoultcult In (Net A#i InIm"5(0)irlru untHhutAeAnIoll Iuinna[| 0i ( = 45euie Mhtayloemdnaue|"4(9)
rchllonehr Mlok Tal ALallon Gum Jor % (r)ad /o lor , [0) ) Knlen Fm relationshlp oret DracI Ant I corrtant +4 Ure Ectatu sh scn Wneed "nleysnd Slnce tno cerrau Lit 4yl eti Gulite costd, suk mt echanged betoen Iht Loo tanks Mtcin datru Aere Ltaetolt soltu Ilc Inauivulus Eoblem 0 imAmoult cult I...
5 answers
QuestionThe points scored by different children in game are categorized in three teams are given below By using ANOVA test whether the means of the three populations are same or not:TeamTeam 2Team=5Ey 100 Ey =888(Marks 10)
Question The points scored by different children in game are categorized in three teams are given below By using ANOVA test whether the means of the three populations are same or not: Team Team 2 Team =5 Ey 100 Ey =888 (Marks 10)...
5 answers
1. Consider the equations of 3 planes:x-α^2z = 4-αy+2z =1x+2y+3z = 5(i) Write an augmented matrix for this system of equations andperform row operations till in reduced row echelon form.(ii) Find values of α for which there are/isA. no solutions.B. a point solution.C. a line of solutions.
1. Consider the equations of 3 planes: x-α^2z = 4-α y+2z =1 x+2y+3z = 5 (i) Write an augmented matrix for this system of equations and perform row operations till in reduced row echelon form. (ii) Find values of α for which there are/is A. no solutions. B. a point solution. C. a line of sol...
5 answers
BH; THF2H,O> OH"HgSO z H,SO_ H,OLHg(OAc)> H,o 2. NaBILNBS; LightCH,l} Zn(Cu)
BH; THF 2H,O> OH" HgSO z H,SO_ H,O LHg(OAc)> H,o 2. NaBIL NBS; Light CH,l} Zn(Cu)...
5 answers
Suppose that F (x) = Vf (g (x)) and g (3) = 5,& (3) = -1,f(3) = 9,f(5) = 4f' (3) = 6,andf' (5) = -2. Find F' (3). 0 A 422E -1
Suppose that F (x) = Vf (g (x)) and g (3) = 5,& (3) = -1,f(3) = 9,f(5) = 4f' (3) = 6,andf' (5) = -2. Find F' (3). 0 A 4 2 2 E -1...
5 answers
Solve the followin9 Sy Stem 0 f GE(2) Xi + X2 + Xz Xi Xz Rz = Rz-R Ri : Ri - Rz (ael Rz' = Ra - R z X3 'leading oneNo SolutionList 0 f notation
Solve the followin9 Sy Stem 0 f GE(2) Xi + X2 + Xz Xi Xz Rz = Rz-R Ri : Ri - Rz (ael Rz' = Ra - R z X3 'leading one No Solution List 0 f notation...

-- 0.020809--