anonymous
  • anonymous
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
Mathematics
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anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. 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. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • 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
  • 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
  • jim_thompson5910
So what do you get when you translate "Produce at least 20 of product #2"

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anonymous
  • anonymous
y>= 20?
jim_thompson5910
  • jim_thompson5910
you got it
jim_thompson5910
  • jim_thompson5910
Therefore, your system should be x >= 30 y >= 20 3x+5y <= 340
anonymous
  • anonymous
dude, thank you so much! :D
jim_thompson5910
  • jim_thompson5910
yw, the only thing left to do is graph do you know how to do that?
anonymous
  • anonymous
not with inuqualitites.. help?
jim_thompson5910
  • 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
  • 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
  • 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
  • jim_thompson5910
all 3 regions overlap to form the final shaded region
anonymous
  • anonymous
how would I do 3x+5y <= 340?
jim_thompson5910
  • 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
  • anonymous
Youre amazing! xD
jim_thompson5910
  • jim_thompson5910
thx, now you just need one more point to graph 3x+5y = 340
anonymous
  • anonymous
x=30, right?
anonymous
  • anonymous
hold on, it didn't post part of the directions..
jim_thompson5910
  • jim_thompson5910
alright
anonymous
  • 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
  • jim_thompson5910
same problem or different one entirely?
anonymous
  • anonymous
Same
anonymous
  • anonymous
I think.. It was just the directions continued
jim_thompson5910
  • jim_thompson5910
alright thx
jim_thompson5910
  • 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
  • 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
  • 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
  • jim_thompson5910
here is the xy axis |dw:1358723166719:dw|
jim_thompson5910
  • jim_thompson5910
now here I'm going to add on the graphs of x = 30, y = 20, and |dw:1358723212768:dw|
jim_thompson5910
  • jim_thompson5910
the shaded region is here |dw:1358723376880:dw| and it includes the surrounding (triangular) boundary
anonymous
  • anonymous
x would be (30,0) and y would be (0,20) right?
jim_thompson5910
  • jim_thompson5910
what do you mean
anonymous
  • anonymous
for x>=30 I would graph (0,30) ?
anonymous
  • anonymous
i mean (30,0)
jim_thompson5910
  • jim_thompson5910
yes you would use any points with an x coordinate of 30
anonymous
  • anonymous
ok cool
jim_thompson5910
  • jim_thompson5910
were you able to find the points of intersection?
anonymous
  • anonymous
still working on it
jim_thompson5910
  • jim_thompson5910
alright
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
I have the points so far
jim_thompson5910
  • jim_thompson5910
this is what I got (see attached)
1 Attachment
anonymous
  • anonymous
So I connect them and shade the middle right?
jim_thompson5910
  • jim_thompson5910
those points you got look like they need more points to be able to draw the 3 lines
jim_thompson5910
  • jim_thompson5910
take a look at what I posted and see if that makes sense or not
anonymous
  • anonymous
It wont open
jim_thompson5910
  • jim_thompson5910
odd, it should work with geogebra your file worked
jim_thompson5910
  • jim_thompson5910
here is a screenshot of the graph
1 Attachment
anonymous
  • anonymous
So I need to (30,0) and (30,4)
anonymous
  • anonymous
more points
jim_thompson5910
  • jim_thompson5910
yes 2 points per line
anonymous
  • anonymous
k I have
1 Attachment
anonymous
  • anonymous
the screen shot worked (:
jim_thompson5910
  • jim_thompson5910
ok great, the upper horizontal line should be diagonal like in the pic i posted
anonymous
  • anonymous
so how do I fix that?
jim_thompson5910
  • jim_thompson5910
make it go through the points (0,68) and (30,50)
anonymous
  • anonymous
Ive never used GeoGebra before
anonymous
  • anonymous
k
jim_thompson5910
  • 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
  • anonymous
K I got
1 Attachment
jim_thompson5910
  • jim_thompson5910
ok you got all 3 lines nailed down correctly
jim_thompson5910
  • jim_thompson5910
the shaded region will be the triangle in the middle and it will include the boundary
anonymous
  • anonymous
Ok awesome! ..how do I shade it?
jim_thompson5910
  • jim_thompson5910
like shown in the attachment
1 Attachment
jim_thompson5910
  • 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
  • anonymous
Thank you so much!
jim_thompson5910
  • 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
  • anonymous
So the shaded region would be P = 10x + 15y, right?
jim_thompson5910
  • 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
  • jim_thompson5910
no it won't, the shaded region is done
jim_thompson5910
  • jim_thompson5910
what are the points of intersection
anonymous
  • anonymous
Oh! I plug in the x and y coordinates into P = 10x + 15y
jim_thompson5910
  • jim_thompson5910
yep, you find the x,y coordinates of these three intersections
1 Attachment
jim_thompson5910
  • jim_thompson5910
then you plug them into P = 10x + 15y
anonymous
  • anonymous
Okays thank you (:
jim_thompson5910
  • jim_thompson5910
the ordered pair that gives you the largest value of P is the winner
anonymous
  • anonymous
cool

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