#1
Im stuck on this Linear Programming Activity. Please help:

A table manufacturer has two warehouses, one in Austin and the other in Tyler. These warehouses supply stores in Ft. Worth and Houston. Every table sold at these two stores must come from one of the two warehouses. On a particular day, the Houston store gets 10 table orders and the Ft. Worth store gets 12 table orders. The Austin Warehouse has 15 tables available and the Tyler warehouse has 10 tables available. The cost of shipping one table is $50 from Austin to Ft. Worth, $40 from Austin to Houston, $30 from Tyler to Ft. Worth and $60 from Tyler to Houston. Create a diagram of this information. How many tables should be shipped from each warehouse to fill the orders for the day at a minimum cost?


My teacher gave me the 4 constants:

X ≤ 12
Y ≤ -X+15
Y < 10
Y ≥ -X+12

So I graphed those points, and got these coordinates for the vertices:
(12,0)
(12,3)
(2,10)
(5,10)


Now here's the part I am stuck on; I need to find the objective function (includes the money part) so i can plug the coordinates into it, and find the minimum cost.

Can anyone help me?

All I have so far is:

Shipping for 1 Table $50 Austin to Ft. Worth
Shipping for 1 Table $40 Austin to Houston
Shipping for 1 Table $30 Tyler to Ft. Worth
Shipping for 1 Table $60 Tyler to Houston


But I need to put that into a function so i can plug the coordinates that i got into (X,Y); so i can get the Minimum cost.

Please help!!
Last edited by Camaro_IRocz at Sep 17, 2008,
#3
i failed algebra


luckly im homeschooled
Emerse your soul in love


You used to be alright What happened?


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#4
What is this grade 9? Just think about it.

It's a linear problem, and your brain is designed to understand linear concepts.
#5
Quote by tona_107
What is this grade 9? Just think about it.

It's a linear problem, and your brain is designed to understand linear concepts.

Its grade 11. I cant figure out how to put the shipping into a Objective function.
#7
holy crap my algebra 2 class is WAY easier than that stuff. it's pretty much just a second year of algebra 1
#8
Quote by Skierinanutshel
use the liner equation and the point-slope form to formulate an equation

... is that what you want to know?

No, im trying to find a function that looks like this: 4x+3y=12 (not as simple, but is similar because it needs a y, and an x)

Basically, i need a formula to plug the coordinates into. but i cant figure out how to get it.
#9
I'm on it...wait a minute.

Do you want a picture of the graph ??
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#11
Quote by X-Boy
I'm on it...wait a minute.

Do you want a picture of the graph ??

I have the graph, it looks like a Trapezoid. and i got the coordinates already, but i need to find an objective function using the shipping things to plug the coordinates into.
#12
Quote by Camaro_IRocz
I have the graph, it looks like a Trapezoid. and i got the coordinates already, but i need to find an objective function using the shipping things to plug the coordinates into.


Ooooooooh.
Make four formulas, using your coordinates, and then combine them into one equation that has 4 x values. Make sure you state your restrictions.
That should work.
#13
Do you have the answer to the question so that i can cross check my equation ?
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#14
Quote by tona_107
Ooooooooh.
Make four formulas, using your coordinates, and then combine them into one equation that has 4 x values.
That should work.

I see what your saying but how would i go doing that?

Like (12,0) is one for an example. How would i put that into an equation?
#15
Quote by X-Boy
Do you have the answer to the question so that i can cross check my equation ?

What do you mean? Which question?
#16
Umm your question in the first post...did your teacher give you the minimum cost or the final answer to the question so that you know if you did it correct ?

EDIT: And in your constraints what did you consider as x and what as y..
Quote by blynd_snyper
yes we all need answers to xboys questions hurry up goddam it


Quote by Kankuro
Damn you X-Boy!!!


Founder And Member Of The " I Don't Masturbate Club "

TURNED 18 TODAY !!! (22/02)
Last edited by X-Boy at Sep 17, 2008,
#17
I'm pretty good at sleeping through algebra 2 classes. if you need any pointers just ask
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#19
Quote by X-Boy
Umm your question in the first post...did your teacher give you the minimum cost or the final answer to the question so that you know if you did it correct ?

No, im trying to find the minimum cost, but i need an equation to plug the coordinates into to find the minimum. For example:

Funtion = 2x + 2y =

(12,0)

2(12)+2(0)= 24

(12,3)

2(12)+2(3)= 30

(2,10)

2(2)+2(10)= 24

(5,10)

2(5)+2(10)= 30

The max is 30, the min is 24.
#20
Quote by X-Boy
Umm your question in the first post...did your teacher give you the minimum cost or the final answer to the question so that you know if you did it correct ?

EDIT: And in your constraints what did you consider as x and what as y..


for the contraints:

x were tables going to fort worth (from both tyler and austin)

an the y were tables going to houston (from both tyler and austin)
#21
Quote by GabeT347
hahah
i JUST did this shit. ok take alll that crap you got and put it into point slope form ( y=mX+B) then change that into standard form ( which is the type of function you said u were looking for) . Standard form is Ax+By=b. So to change say the point 6,0 to that form 1. find the slop of the line and the y intercept. make it in to the y= mX+ b and then the standard. i think thas it haha.

but where does the money come in effect
#23
K dude i really think the way you've taken your constraints are wrong.

Look consider it this way.

The amount of tables trasported from Austin to Ft.Worth is x and the amount from Austin to Houston is y.

So the amount transported from Tyler to Ft.Worth is 12-x and the amount from Tyler to Houston is 10-y.

That solves everything.

Your constraints are,

x+y<=15
22-x-y<=10
x>=0
y>=0

Anyways i think the equation you need to minimize is x-y+48

Your answer according to your points would be (2,10)

Get back with the correct answers...wanna see if i got it right
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TURNED 18 TODAY !!! (22/02)
Last edited by X-Boy at Sep 18, 2008,