Re: These Math books are something else......Please Help me
Hello, passionflower_40!
You have to baby-talk your way through these problems . . .
The Ozark Furniture Company can obtain at most 8000 board feet of oak lumber
for making Round and Square tables.
The tables must be stored in a warehouse that has at most 3850 ft<sup>3</sup> of space available for the tables.
A Round table requires 50 board feet of lumber and 25 ft<sup>3</sup> of warehouse space.
A Square table requires 80 board feet of lumber and 35 ft<sup>3</sup> of warehouse 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.
Let R = number of Round tables, and S = number of Square tables.
Each Round table takes 50 feet of lumber, a total of 50R feet.
Each Square table takes 80 feet of lumber, a total of 80S feet.
The total lumber needed is: 50R + 80S feet
. . But we are told that this is limited to 8000 feet.
There is one inequality:
.50R + 80S .< .8000
Each of the R round tables needs 25 ft<sup>3</sup> of space, a total of 25R ft<sup>3</sup>.
Each of the S square tables need 35 ft<sup>3</sup> of space, a total of 35S ft<sup>3</sup>.
The total space needed is: 25R + 35S.
. . But we are told that this is limited to 3850 ft<sup>3</sup>.
There is the other inequality:
.25R + 35S .<u><</u> .3850
To graph the inequalities, we first graph the equations (lines).
First, we assume that: R <u>></u> 0 and S <u>></u> 0; the region is in quadrant 1.
The line 50R + 80S = 8000 has: R-intercept (160,0) and S-intercept (0,100).
The line 25R + 35S = 3850 has: R-intercept (154,0) and S-intercept (0,110).
Graph each line and shade the region <u>below</u> it.
The common shaded region is the required graph.
Every point in that region (and on its border)
. . has coordinates (R,S) that satisfy the restrictions.
