Question

Anne has decided to buy no more than 50 dining-room tables to sell at her furniture store. She has also decided to restrict herself to buying only oak and mahogany tables. Anne wants to buy at least 10 oak tables and at least 15 but no more than 23 mahogany tables.

Write a system of linear Inequalities to represent the constraints Anne has set.

Anna ears a profit of $250 on each oak table that she sells and a profit of $175 on each mahogany table that she sells. Write the objective function that Anne would use to maximize her profit from the tables.

Answer 1

Graph the set of constraints and find the vertices to test in the objective function.

Answer 2

Can anyone help? My gf asked me to help her out but Im totally lost...

Answer 3

Let the number of oak tables she's gonna buy and the number of mahogany tables she's gonna buy be \(o\) and \(m\) respectively.
\[o\ge10\]\[15\le m\le23\]

Answer 4

I can help you out! Alright, so first, what do you think a constraint and objective function are? Nonsense words made up to make people believe math is difficult.

What's a constraint in normal use? Maybe a bunch of chains holding you down, constraining you? Similarly here, what's holding us back from just buying a billion tables? Well, at the very beginning they've stated that they would buy no more than 50 tables. Do you see any other possible constraints?

Now to put it more mathematically, let's give names to things with variables so that we can more quickly and easily see everything.

T=total number of tables
K=oak tables (I didn't want to use O since it looks like zero)
M=mahogany

Can you make any kind of formulas relating these three quantities? I'll keep helping you along and if you can think ahead of me and tell me your guesses of what you and your gf are thinking about we can understand this together.

Answer 5

Okay...Kinda a trick question then..Yeah I see where you are coming from with the constraints aka "50 tables"...I've been helping her since 1 today so we are both pretty shot haha...Im assuming that \[0 \ge 10 \] and \[15 \le m \le 23\] correct? @Kainui

Answer 6

Thats some formula we thought of but I don't see how it ties back up and how we can use it.

Answer 7

It asks us to..Write a system of linear Inequalities to represent the constraints Anne has set...But we have no equations except those.

Answer 8

that's exactly what i've written lol

Answer 9

Sorry lol already had that down. Should have mentioned that.

Answer 10

Well she had it down.

Answer 11

ok, please kindly close it :)

Answer 12

Close what this post? I still cant solve the rest...Okay then haha

Answer 13

Sorry my notification thing was messed up and didn't know this was going on!

Answer 14

oh lol i thought you already solved it

Answer 15

Lemme catch up with where you guys are real quick.

Answer 16

No she just thought of some formulas. We dont understand how we could use them though. We kinda understand what they want but not how to get it.
Especially the graphing part..

Answer 17

So similarly with the number of tables, let's just realize that when they say "profit per table" it's just like "miles per hour" If you multiply either of these with "tables" or "hours" you get profit and distance respectively. I hope that's not too confusing.

So when they say that they make 250 per oak and 175 per mahogany that means our total profit will be:

P=250*K+175*M

Now remember, the other equations you made earlier are still in effect and you can't just plug in like 50 oak tables and 10 mahogany, since you have certain limitations. So by following those limitations you can see how price varies depending on your constraints. Maybe you can guess what a graph might look like? Amount of one table on one axis with price on the other axis.

Something like that, you could use oak. Just make sure you don't graph things outside of your constraint!

Answer 18

Wow...Didnt think an algebra problem could be so tough...Seriously I've gone through calculus and that is easier then this! haha

Answer 19

Actually you do stuff like this whenever you do optimization in calculus, it's just that this is more discreet so you have to do each point. More labor intensive on this one.

Answer 20

Ahh makes sense. lol

Answer 21

Well haha my friend James just came over and he showed us the rest. xD Thanks though man! :D