that1chick
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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that1chick
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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
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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
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So what do you get when you translate "Produce at least 20 of product #2"
that1chick
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y>= 20?
jim_thompson5910
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you got it
jim_thompson5910
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Therefore, your system should be
x >= 30
y >= 20
3x+5y <= 340
that1chick
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dude, thank you so much! :D
jim_thompson5910
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yw, the only thing left to do is graph
do you know how to do that?
that1chick
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not with inuqualitites.. help?
jim_thompson5910
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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
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To graph y >= 20, you
* graph the horizontal line y = 20
* make it a solid line
* shade above the solid line
jim_thompson5910
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to graph 3x+5y <= 340, you
* graph the line 3x+5y = 340
* make it a solid line
* shade below the line
jim_thompson5910
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all 3 regions overlap to form the final shaded region
that1chick
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how would I do 3x+5y <= 340?
jim_thompson5910
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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)
that1chick
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Youre amazing! xD
jim_thompson5910
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thx, now you just need one more point to graph 3x+5y = 340
that1chick
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x=30, right?
that1chick
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hold on, it didn't post part of the directions..
jim_thompson5910
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alright
that1chick
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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
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same problem or different one entirely?
that1chick
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Same
that1chick
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I think.. It was just the directions continued
jim_thompson5910
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alright thx
jim_thompson5910
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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
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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
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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
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here is the xy axis
|dw:1358723166719:dw|
jim_thompson5910
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now here I'm going to add on the graphs of x = 30, y = 20, and
|dw:1358723212768:dw|
jim_thompson5910
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the shaded region is here
|dw:1358723376880:dw|
and it includes the surrounding (triangular) boundary
that1chick
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x would be (30,0) and y would be (0,20) right?
jim_thompson5910
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what do you mean
that1chick
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for x>=30 I would graph (0,30) ?
that1chick
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i mean (30,0)
jim_thompson5910
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yes you would use any points with an x coordinate of 30
that1chick
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ok cool
jim_thompson5910
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were you able to find the points of intersection?
that1chick
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still working on it
jim_thompson5910
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alright
that1chick
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that1chick
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I have the points so far
jim_thompson5910
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this is what I got (see attached)
that1chick
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So I connect them and shade the middle right?
jim_thompson5910
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those points you got look like they need more points to be able to draw the 3 lines
jim_thompson5910
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take a look at what I posted and see if that makes sense or not
that1chick
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It wont open
jim_thompson5910
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odd, it should work with geogebra
your file worked
jim_thompson5910
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here is a screenshot of the graph
that1chick
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So I need to (30,0) and (30,4)
that1chick
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more points
jim_thompson5910
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yes 2 points per line
that1chick
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k I have
that1chick
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the screen shot worked (:
jim_thompson5910
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ok great, the upper horizontal line should be diagonal like in the pic i posted
that1chick
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so how do I fix that?
jim_thompson5910
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make it go through the points (0,68) and (30,50)
that1chick
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Ive never used GeoGebra before
that1chick
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k
jim_thompson5910
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or you can simply type in 3x+5y = 340 into the input bar and it will graph the line 3x+5y = 340 for you
that1chick
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K I got
jim_thompson5910
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ok you got all 3 lines nailed down correctly
jim_thompson5910
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the shaded region will be the triangle in the middle and it will include the boundary
that1chick
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Ok awesome! ..how do I shade it?
jim_thompson5910
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like shown in the attachment
jim_thompson5910
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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
that1chick
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Thank you so much!
jim_thompson5910
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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
that1chick
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So the shaded region would be P = 10x + 15y, right?
jim_thompson5910
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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
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no it won't, the shaded region is done
jim_thompson5910
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what are the points of intersection
that1chick
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Oh! I plug in the x and y coordinates into P = 10x + 15y
jim_thompson5910
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yep, you find the x,y coordinates of these three intersections
jim_thompson5910
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then you plug them into P = 10x + 15y
that1chick
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Okays thank you (:
jim_thompson5910
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the ordered pair that gives you the largest value of P is the winner
that1chick
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cool