no id - Chat started on:  Nov 16, 2007 9:51:47 PM
[9:51 PM] Corey Couillard has entered the room
[9:51 PM] Kate Sims has entered the room
[9:51 PM] This room is not anonymous.
[9:51 PM] ziizoo admin: Session started on Fri Nov 16 21:53:02 EST 2007
[9:51 PM] Kate Sims: Hi Corey
[9:52 PM] Kate Sims: Okay, first we need to write the inequalities for the "constraints"
[9:52 PM] Corey Couillard: Hi Kate, thank you for joing
[9:52 PM] Corey Couillard: ok
[9:52 PM] Kate Sims: Actually, let's define variables first
[9:53 PM] Corey Couillard: r = reg hd, b=beef
[9:53 PM] Kate Sims: Sounds good.  Can you write the "constraints"?
[9:55 PM] Kate Sims: Good.  I saw you fix one mistake... do you see where the same thing happened again?
[9:56 PM] Kate Sims: Yep, very good
[9:56 PM] Kate Sims: Okay, what's the objective function (the equation we're maximizing)?
[9:58 PM] Kate Sims: Great!
[9:58 PM] Kate Sims: The next thing is to graph your two inequalities
[9:59 PM] Kate Sims: The easiest way is to find the intercepts
[9:59 PM] Kate Sims: Do you have a preference of which variable we're going to call x?
[10:00 PM] Corey Couillard: no
[10:00 PM] Kate Sims: Okay, I already sketched it out, so let's make "r" our x and "b" our y
[10:00 PM] Kate Sims: One way to graph is to find the intercepts.  In the first equation, if b = 0 then what is r?
[10:02 PM] Corey Couillard: 300
[10:02 PM] Kate Sims: That's for the second inequality, right?
[10:02 PM] Corey Couillard: 0,300
[10:03 PM] Kate Sims: Right idea, except I declared "r" to be x
[10:03 PM] Corey Couillard: sorrry, I am getting confused 0,200
[10:04 PM] Kate Sims: Okay, wait.  Which inequality are we doing, and which variable are we plugging in zero for?
[10:05 PM] Kate Sims: That looks good.  And then plug in b = 0 into #1 to get r
[10:08 PM] Corey Couillard: is that what you want me to do
[10:08 PM] Kate Sims: Let me show you...
[10:09 PM] Kate Sims: How would you get r?
[10:11 PM] Kate Sims: I'm not sure where the 150 comes from.  I agree that you should do 200 divided by 1/2
[10:13 PM] Kate Sims: If you want to delete something, you can click on the button to the left of the garbage can, draw a box around whatever it is, then hit "garbage can"
[10:14 PM] Kate Sims: You can go to Edit  and then Undo if you want that back...
[10:20 PM] Kate Sims: Rember that to divide by a fraction you flip and multiply. 
[10:21 PM] Kate Sims: Do you see what I mean?
[10:23 PM] Kate Sims: Good
[10:23 PM] Kate Sims: So we've determined in the first inequalitiy that when r = 0 b = 200, the point (0, 200) and when b = 0, r = 400, the point (400, 0).  So you can plot those points and connect them to make the line.
[10:24 PM] Corey Couillard: ok
[10:26 PM] Corey Couillard: Isn't 400, 0 a false statement given we only 150 lbs of pork so the max of reg would be 300
[10:27 PM] Kate Sims: Right, but we're going to consider each inequality separately.  So graph the first line, and then we'll worry about the second inequality
[10:29 PM] Kate Sims: By the way, the reason I had you do intercepts (plugging in 0 and solving for the other variable) is on the max/min problems that have bigger numbers, the slope can be messy to graph.  For example, if you got b by itself in the first inequality you'd have B <= -(1/2)R + 200 and how would you know how to go down 1 and over 2 if you're going by hundreds?!?
[10:30 PM] Corey Couillard: rise/run
[10:31 PM] Corey Couillard: right
[10:31 PM] Kate Sims: Now let's look at the second inequality.  Since there's only one variable here, let's just get it by itself
[10:32 PM] Corey Couillard: you would move the 1/2 over to the 150 side to get r alone
[10:32 PM] Kate Sims: Good, show me
[10:36 PM] Kate Sims: Yes, good.
[10:36 PM] Kate Sims: How would you graph the line r = 300?
[10:36 PM] Kate Sims: That's looking like b = 300
[10:39 PM] Kate Sims: Okay, now we have the lines (1/2)R + 1B = 200 and (1/2)R = 150.  Where can we shade to show everywhere that ( (1/2)R + 1B <=200 and (1/2)R <= 150?
[10:40 PM] Kate Sims: The second equation we said means that r <=300.  What is r where you shaded?
[10:42 PM] Kate Sims: In other words, r is too big where you shade.  What side of that vertical line is all the r's less than 300?
[10:43 PM] Corey Couillard: i don't understand what your saying
[10:44 PM] Kate Sims: I'm going to eyeball a point in the region you shaded and give the coordinates
[10:45 PM] Kate Sims: That point is shaded, but it can't be because r is 320, and our rule says that r <= 300
[10:46 PM] Corey Couillard: where i scrimbled in i would in my graph and get the coordinates to the triangle aroud the triangle.
[10:46 PM] Kate Sims: I agree we're going to get the coordinates, but you have the wrong region scribbled in.  That was my point.
[10:46 PM] Corey Couillard: i would shade in my graph and get the coordinates to the triangle my bad
[10:47 PM] Corey Couillard: how about there
[10:47 PM] Kate Sims: I'm going to use the cute green shaded polygon tool to make it pretty
[10:48 PM] Kate Sims: Good.  Okay, now we need to find the coordinates of the corners
[10:49 PM] Corey Couillard: i have no clue how to find the coordinates 
[10:49 PM] Kate Sims: Well, 3 of them are really easy.  What about the top one?
[10:49 PM] Corey Couillard: 200
[10:49 PM] Kate Sims: Should have 2 coordinates
[10:50 PM] Corey Couillard: (0,200)
[10:50 PM] Kate Sims: Okay, what about the bottom left?
[10:50 PM] Corey Couillard: (300,0)
[10:51 PM] Kate Sims: Actually, that's the bottom right corner, but same difference :)
[10:52 PM] Corey Couillard: (0,0)
[10:52 PM] Kate Sims: Yep.  Okay, now for the "hard" one
[10:52 PM] Kate Sims: We're looking for where those 2 lines cross
[10:52 PM] Kate Sims: In other words, where (1/2)R + B = 200 and R = 300
[10:53 PM] Kate Sims: Hint:  it's a system of equations, but in this case it's very easy because you have R and can just plug it into the first equation to get B
[10:54 PM] Corey Couillard: 50
[10:54 PM] Kate Sims: Yes!  Label that point
[10:55 PM] Kate Sims: Now, all you have to do is plug each point into the objective function and see which one is best
[10:56 PM] Corey Couillard: When I label 50 do you mean (150,50) which would be in the colored in area
[10:57 PM] Kate Sims: B = 50, but what was R? 
[10:58 PM] Corey Couillard: 300
[10:59 PM] Kate Sims: Yes, so it's the point (300, 50), which is the 4th corner (which is what we were trying to get!)
[11:00 PM] Kate Sims: Okay,  so now you can plug each of those corner points into the objective function
[11:02 PM] Kate Sims: In other words, into .3R + .4B
[11:05 PM] Corey Couillard has left