Expert: Richard J. Raridon - 12/6/2004

Question
A furniture company can obtain at most 8000 board feet of oak lumber for making round and rectangular tables. The tables must be stored in a wharehouse that has at most 3850 ft³ of space available for the tables. A round table requires 50 board feet of lumber and 25 ft³ of wharehouse space. A rectangular table requires 80 board feet of lumber and 35 ft³ of wharehouse space. Write a system of inequalities that limits the possible number of tables of each type that can be made and stored. Graph the system.

I have come up with part of the answer (I think!)

The two inequalities:
If x is the number of round tables and y rectangular tables, then: 50x + 80y are less than or equal to 8000 (I'm not sure how to make the less than sign here with the equal sign under it).
If x is the amount of space that the round tables take and y is the rectangular, then:
25³x + 35³y is less than or equal to 3850³
If these are right, how do you graph them (I know it's with the slope intercept form, but I don't know how to do that very well) Either way, will you please break it down for me step-by-step so I can understand? Thank you very much!

Answer
They can make 160 round tables but could only store 154 of them. They can make 100 rectangular tables but could store up to 110.  
So you have 50x +80y <= 8000, plus x <= 154
25x + 35y <= 3850, plus y <= 100
To plot 50x +80y = 8000 (forget the < for now), simply put in a value for y, solve for x, and plot (x,y)
A few points are (0,100), (20,87), (50,68), (154,3)
Do the same thing for 25x +35y = 3850
A few points are (154,0), (100,38), (14,100)