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- anonymous

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- katieb

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- phi

I just noticed the last line: If you must order at least one of each type of table,
because without that line I was not getting any of your choices.
Can you try to sketch the relations?
Let x be the number of type A and
y be the number of type B
You can order no more than 190 tables this month.
that means the sum of x and y must be less than or equal to 190
x+y≤ 190
put this into slope-intercept form: y ≤ -x + 190
plot the line y= -x + 190
shade the area under this line (this is where y is less than the line)
can you do that?

- anonymous

I'll try :) one sec

- phi

It only shows a bit of the graph.
By hand:
|dw:1358269570252:dw|

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## More answers

- anonymous

OK so what does this tell me now? sorry I'm dumb :(

- phi

We don't go below x=0 (we can't order less than 0) same for y
that triangle represents all (x,y) pairs of orders where x+y ≤ 190 (and x+y≥0 we can't order less than 0)
if you go outside the triangle you will order too many or a negative number. Neither is allowed.

- phi

you need to make at least $4,610 profit on them
It would be good if you could write down the relation (mathematical expression) for this. Hero posted it, but you should try. The profit will be the number of type A's times the profit per type A plus # of B's times profit of a B
this sum must be ≥ 4610
Can you write down the expression?

- anonymous

29a + 19b >_ 4610

- phi

ok, but use x and y, because we have to plot this...

- anonymous

ok :) 29x + 19y >_4610

- phi

can you put it into slope-intercept form?

- anonymous

IDK sorry

- phi

slope intercept form is y ≥ mx + b
in other words, y is by itself on the left.
First step is add -29x to both sides. Just write -29x on both sides
what do you get?

- anonymous

y=x+19>_4610 IDk

- phi

don't make things up. start with
29x + 19y >= 4610
write -29x on both sides:
-29x + 29x + 19y >= -29x + 4610
on the left side you have 29x and -29x (think: 29 x's take away 29 x's. I get no x's)
19y ≥ -29x +4610
now divide both sides by 19. That means divide each term on both sides by 19
what do you get?

- anonymous

y≥ -29/12x + 4610/19

- phi

I assume that 12 is a typo?

- anonymous

ohh I mean 19

- phi

now, let's change into decimals (only a few digits). Roughly we get
y ≥ -1.53 x + 242.6
now plot this line. Y ≥ means shade all the Y above the line.
Can you plot this line?

- anonymous

I have no idea:(

- phi

for
y ≥ -1.53 x + 242.6
we first plot
y = -1.53x +242.6
if we set x to 0, what is y ?

- anonymous

y ≥ 242.6

- phi

Ok, x=0, y = 242.6 (0,242.6) is one point on the line
can you plot this point ?

- anonymous

idk how

- anonymous

|dw:1358271480089:dw|

- phi

yes, that looks good
See http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/plot-ordered-pairs
if you need a refresher.
now lets find y when x = 100
y = -1.53x +242.6
replace x with 100
y = -1.53*100 + 242.6
what do you get ?

- phi

I picked x=100 because it is easy to multiply by 100. we could pick any x, but x near or inside our triangle makes sense.

- anonymous

y= 395.6

- phi

-1.53*100 is a negative number. try again

- anonymous

89.6

- phi

that means (100,89.6) is on the line.
can you plot this point ? go to x=100 and move up about 90.

- anonymous

|dw:1358272059574:dw|

- phi

now connect the dots (or x's in this case)
|dw:1358272145701:dw|

- anonymous

d.)100 of type A; 90 of type B

- phi

I shaded the area above the line, because that is where y ≥ to the line
The black shaded area is everywhere where you get the needed profit
(remember profit must be ≥ 4610)
We also must be below the red line. To meet both requirements, we must be in the lower triangle.

- anonymous

ahhhh ok I'm confused now...what is the answer?

- phi

Once you get the "feasible" region, you check the "corners" for the (x,y) pair that matches your requirement.
In this case, the bottom two spots have y=0 and the statement
If you must order at least one of each type of table means we can rule out those points
we have to find the intersection of the two lines. but we see by eyeball it is 100, 90

- anonymous

so its AorD :D

- phi

A is x in our graph. and B is y
Here is how to find where the lines cross:
you start with
y= -x + 190
y = -1.53x +242.6
when they meet they have the same y values. we set
-x + 190 = -1.53x +242.6
add 1.53x to both sides (you should learn how to do this, btw)
1.53x - 1x + 190= -1.53x + 1.53x +242.6
on the left we get 0.53x+190 and on the right 242.6:
0.53x +190 = 242.6
add -190 to both sides
0.53x +190-190= 242.6-190
0.53x = 52.6
divide both sides by 0.53, and x = 99.2
looking at our graph, we want x bigger than this (we have to buy a whole table)
x=100
and
x+y =190
replace x with 100: 100+y=190
add -100 to both sides: 100-100+y= 190-100
y=90
In a harder problem, we would use these x,y numbers in the cost equation, and find the (x,y) pair (of the three corners) that gives the lowest cost.
here, we just need to find the top "corner" because the bottom 2 are ruled out by the question (we must buy some of both types, so 0 is not allowed)

- anonymous

So the answer is A :) thank you so much for spending the time on teaching me :p I really appreciated

- phi

I think you can do this stuff, but you have skimped so much in learning all the details that it is difficult to do a problem like this where you have to remember how to do lots of things: plot, solve equations, etc.

- phi

Personally, I would pick just one area (example: putting equations into slope-intercept form), and watch a video at Khan

- anonymous

ok I'll try that thanx again :)

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