Question

.

Answer 1

Would this be a good scenario or no?

Answer 2

sounds ok

Answer 3

put limits on x (for example, you have only 10 shirts)
so x<10 could be a relation
do the same for y
then plot the 3 lines
x=10
y= whatever
4x+5y=40
and shade in the region where you make 40 or more dollars

Answer 4

it is not a very interesting problem, but it's ok.
you might also restrict x and y to be 0 or more (no negative numbers of shirts/shorts allowed)

Answer 5

wait in the beginning I said I wanted to make at least $40 dollars. So would it be 4x + 5y >= 40? I forgot to add the = sign initially.

Answer 6

Idk I feel like I should come up with a better one that is a little longer....

Answer 7

Thanks for helping me through this though. I really appreciate it.

Answer 8

I guess I could just graph it and find the y and x intercepts to make it look a little longer and more interesting.

Answer 9

People (who use math for a living) have all kinds of problems... but generally, the problems are "given"... coming up with a problem that is interesting is difficult.

Answer 10

Yeah, I was trying to come up with a more complicated one, but this one will do. I'm going to try and find the y and x intercepts to add more to my answer.

Answer 11

oh, yes. You should definitely plot this, and then explain what the plot tells you.

Answer 12

Okay thank you for helping me. You're awesome :)

Answer 13

also, with shirts, you don't have fractions. x<10 would mean x<=9 which is clearer
I would just use 0<= x<=10
and the same for y

Answer 14

Here is a graph.

Answer 15

Your question is still ok. If you look at the graph, the triangle shape on the right side gives all the combinations of shirt/shorts that you need to sell to make 40 or more

Answer 16

Okay.

Answer 17

but I should still indicate that I only have 10 shirts and 4 pairs of shorts available to sell.

Answer 18

Yes, the y-intercept is 10

when you are done, it should look like this

Answer 19

and the x intercept is 8 I think.

Answer 20

or wait isn't x intercept 10 and y intercept 8? I think I accidentally mixed them.

Answer 21

oops, we did that backwards. y intercept = 8 (when x is 0, you get y=8)

Answer 22

yeah

Answer 23

plot y=4 and x=10
shade in the region above the 4x+5y= 40 line (that is where you make 40 or more)
but below y=4 and to the left of x=10

Answer 24

idk

Answer 25

?
once you find the points (0,8) and (10,0) on the line. you plot them, and "connect the dots" to make the line.

Answer 26

so what I just typed doesn't matter.

Answer 27

so after I graph I have to come up with the solution.

Answer 28

what you typed was not clear.
Here is what you are doing:
1) describe the problem. OK , you did that
2) define the variables, and write the relations OK
3) to solve the problem, plot the relations.
a) to plot the line 4x+5y=> 40, find the x and y intercepts
(you did that) to get (0,8) and (10,0). plot those points, and the line
make the line solid because the relation is >=
b) plot the max x=10 line and y=4 line
4) shade in the solution region.
5) explain what the solution region tells us

Answer 29

if you look at the graph you can see that you must sell 5 or more shirts.

Answer 30

you see it is possible to make 40 without selling any shorts, but to do so, you must sell all 10 shirts.

Answer 31

you see the most you can make is $60 (but that is obvious).

Answer 32

You can count 16 different "solutions" (points in the solution region)

Answer 33

what website is that graph from?

Answer 34

geogebra. You can download it for free. It's nice but it has a "learning curve" to use it.

Answer 35

nice thanks :) I really really appreciate you helping me. I wish I could give you like 10 best responses.

Answer 36

yw