I'm not asking for you to do my work for me, just help me create a system of inequalities please!
• The name of your company
• The type of business (i.e., clothing, electronics, furniture, etc.)
• Two products your company will make
• Assign variables to the two products; please use x and y
• A system of inequalities based on the following information
o Produce at least 30 of product #1.
o Produce at least 20 of product #2.
o Product #1 costs $3 per unit to make.
o Product #2 $5 per unit to make.
o The total production cost cannot exceed $340.
• Graph the system of inequalities
o

- anonymous

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- anonymous

What I have so far:
Beyond the Galaxy
We create trippy clothes. Such as (product #1:) shirts (x) and (product #2:) skirts (y).
30x+20y<=
$3x+$5y<=$340

- jim_thompson5910

x is the number of items of product 1
so when you make the requirement that you must "Produce at least 30 of product #1", this means
x >= 30
So you can produce x = 30, x = 31, x = 32, ... items of product 1 (but nothing less than 30)

- jim_thompson5910

So what do you get when you translate "Produce at least 20 of product #2"

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## More answers

- anonymous

y>= 20?

- jim_thompson5910

you got it

- jim_thompson5910

Therefore, your system should be
x >= 30
y >= 20
3x+5y <= 340

- anonymous

dude, thank you so much! :D

- jim_thompson5910

yw, the only thing left to do is graph
do you know how to do that?

- anonymous

not with inuqualitites.. help?

- jim_thompson5910

to graph x >= 30, follow these steps
Step 1) graph the vertical line x = 30
Step 2) make it a solid line
Step 3) shade to the right of this solid line

- jim_thompson5910

To graph y >= 20, you
* graph the horizontal line y = 20
* make it a solid line
* shade above the solid line

- jim_thompson5910

to graph 3x+5y <= 340, you
* graph the line 3x+5y = 340
* make it a solid line
* shade below the line

- jim_thompson5910

all 3 regions overlap to form the final shaded region

- anonymous

how would I do 3x+5y <= 340?

- jim_thompson5910

plug in x = 0 to get
3x+5y = 340
3*0+5y = 340
5y = 340
y = 340/5
y = 68
So one point on the line 3x+5y=340 is (0,68)

- anonymous

Youre amazing! xD

- jim_thompson5910

thx, now you just need one more point to graph 3x+5y = 340

- anonymous

x=30, right?

- anonymous

hold on, it didn't post part of the directions..

- jim_thompson5910

alright

- anonymous

If Product #1 earns a profit of $10 per unit and Product #2 earns a profit of $15 per unit, find the combination of Product #1 and Product #2 that will maximize profit.
A commercial that could be used to advertise your two products to the general public. You may include a slogan or jingle.

- jim_thompson5910

same problem or different one entirely?

- anonymous

Same

- anonymous

I think.. It was just the directions continued

- jim_thompson5910

alright thx

- jim_thompson5910

Let P = combined profit of products #1 and #2
So "If Product #1 earns a profit of $10 per unit and Product #2 earns a profit of $15 per unit", then
P = 10x + 15y

- jim_thompson5910

The ideal situation is that there is an ordered pair (x,y) that is within the shaded region and makes P as large as possible

- jim_thompson5910

It turns out that this ordered pair is a vertex of the shaded region
ie, it is formed by the intersection of two of the lines

- jim_thompson5910

here is the xy axis
|dw:1358723166719:dw|

- jim_thompson5910

now here I'm going to add on the graphs of x = 30, y = 20, and
|dw:1358723212768:dw|

- jim_thompson5910

the shaded region is here
|dw:1358723376880:dw|
and it includes the surrounding (triangular) boundary

- anonymous

x would be (30,0) and y would be (0,20) right?

- jim_thompson5910

what do you mean

- anonymous

for x>=30 I would graph (0,30) ?

- anonymous

i mean (30,0)

- jim_thompson5910

yes you would use any points with an x coordinate of 30

- anonymous

ok cool

- jim_thompson5910

were you able to find the points of intersection?

- anonymous

still working on it

- jim_thompson5910

alright

- anonymous

##### 1 Attachment

- anonymous

I have the points so far

- jim_thompson5910

this is what I got (see attached)

##### 1 Attachment

- anonymous

So I connect them and shade the middle right?

- jim_thompson5910

those points you got look like they need more points to be able to draw the 3 lines

- jim_thompson5910

take a look at what I posted and see if that makes sense or not

- anonymous

It wont open

- jim_thompson5910

odd, it should work with geogebra
your file worked

- jim_thompson5910

here is a screenshot of the graph

##### 1 Attachment

- anonymous

So I need to (30,0) and (30,4)

- anonymous

more points

- jim_thompson5910

yes 2 points per line

- anonymous

k I have

##### 1 Attachment

- anonymous

the screen shot worked (:

- jim_thompson5910

ok great, the upper horizontal line should be diagonal like in the pic i posted

- anonymous

so how do I fix that?

- jim_thompson5910

make it go through the points (0,68) and (30,50)

- anonymous

Ive never used GeoGebra before

- anonymous

k

- jim_thompson5910

or you can simply type in 3x+5y = 340 into the input bar and it will graph the line 3x+5y = 340 for you

- anonymous

K I got

##### 1 Attachment

- jim_thompson5910

ok you got all 3 lines nailed down correctly

- jim_thompson5910

the shaded region will be the triangle in the middle and it will include the boundary

- anonymous

Ok awesome! ..how do I shade it?

- jim_thompson5910

like shown in the attachment

##### 1 Attachment

- jim_thompson5910

you can use geogebra to do the shading, or you can use paint like I just did (I used the paint bucket) to fill in the correct region

- anonymous

Thank you so much!

- jim_thompson5910

sure thing, you can then easily use geogebra to find the points of intersection
then you need to see which points give you the max profit

- anonymous

So the shaded region would be P = 10x + 15y, right?

- jim_thompson5910

no that has nothing to do with the shaded region
once you find the vertices, you use P = 10x + 15y to test each one

- jim_thompson5910

no it won't, the shaded region is done

- jim_thompson5910

what are the points of intersection

- anonymous

Oh! I plug in the x and y coordinates into P = 10x + 15y

- jim_thompson5910

yep, you find the x,y coordinates of these three intersections

##### 1 Attachment

- jim_thompson5910

then you plug them into P = 10x + 15y

- anonymous

Okays thank you (:

- jim_thompson5910

the ordered pair that gives you the largest value of P is the winner

- anonymous

cool

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