I've been out of High School for twenty years now. When I was in school, I was pretty good in math, but I've lost a lot of the higher stuff I learned through lack of use. Still, up till now, all I ever needed to figure out my daughters' homework was a quick google search or some light reading in their textbook. Now, though, my second daughter is doing things in her 9th grade "Advanced Algebra" class that I can barely grasp the workings of.
The question is below:
Question says this company makes chairs and tables. Tables take 3 hours of carpentry and 2 hours of finishing and make a 35 dollar profit. Chairs take 2 hours of carpentry and 1/2 an hour of finishing and make a 20 dollar profit. They can use up to 108 carpentry hours and 20 finishing hours daily. How many chairs and tables should be made each day to maximize profit?
Now I need help... because she doesn't have a clue how to do it, and I only have the vaguest notions. I need some pointers on figuring out just how to solve this problem so that I can give her the tools to solve it. From googling and looking up "Linear Projection" online, I think I'm supposed to generate some equations for graphing, and then find the intersections, one of which will be the point at which so many tables and so many chairs equal the greatest profit. Where I'm stuck is that I can't seem to figure out just which variables to use and what the equations are I need to be solving!
My first thought was that I needed one equation for tables and another for chairs, with X and Y representing hours of Carpentry and Finishing respectively:
3x + 2y = 35
2x + .5y = 20
I solved these equations for y:
y = (35 - 3x) / 2
y = 40 - 4x
And then I get the feeling I'm heading in the wrong direction.. especially when I start graphing them and things seem to be going in the wrong direction.
Anyway, at this point any help would be vastly appreciated, as I'm thoroughly lost on my own.