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

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Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
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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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