Question

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

Answer 1

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

Answer 2

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)

Answer 3

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

Answer 4

y>= 20?

Answer 5

you got it

Answer 6

Therefore, your system should be

x >= 30
y >= 20
3x+5y <= 340

Answer 7

dude, thank you so much! :D

Answer 8

yw, the only thing left to do is graph

do you know how to do that?

Answer 9

not with inuqualitites.. help?

Answer 10

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

Answer 11

To graph y >= 20, you

* graph the horizontal line y = 20

* make it a solid line

* shade above the solid line

Answer 12

to graph 3x+5y <= 340, you

* graph the line 3x+5y = 340

* make it a solid line

* shade below the line

Answer 13

all 3 regions overlap to form the final shaded region

Answer 14

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

Answer 15

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)

Answer 16

Youre amazing! xD

Answer 17

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

Answer 18

x=30, right?

Answer 19

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

Answer 20

alright

Answer 21

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.

Answer 22

same problem or different one entirely?

Answer 23

Same

Answer 24

I think.. It was just the directions continued

Answer 25

alright thx

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

here is the xy axis

Answer 30

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

Answer 31

the shaded region is here



and it includes the surrounding (triangular) boundary