Question 745742: I need help with the following problem:
A man and his daughter manufacture unfinished tables and chairs. Each table requires 3 hours of sawing and 1 hour of assembly. Each chair requires 2 hours of sawing and 2 hours of assembly. Between the two of them, they can put in up to 12 hours of sawing and 8 hours of assembly work each day. Find a system of inequalities that describes all possible combinations of tables and chairs that they can make daily. Graph the solution set.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A similar problem was posted a few days ago as problem number 743379.
 = number of tables made per day
 = number of chairs made per day
Two obvious constraints are
 and 
The amount of sawing to be done per day would be
 .
The amount of assembling work to be done per day would be
 .
The inequalities above graph as a region of the x-y plane representing all the possible combinations of numbers of tables and chairs that they can make daily.
 The feasibility region is the quadrilateral OABC, bounded by the lines
 (the y-axis)
 (the x-axis)
 (the blue line) and
 (the green line).
To plot the blue and green line, I just found the x- and y-intercepts for each one.
For :
when ,  -->  -->  -->  gives us point D(0,6).
When ,  -->  -->  -->  gives us point C(4,0)
For :
when ,  -->  -->  -->  gives us point A(0,4).
When ,  -->  gives us point E(8,0).
The intersection of the 2 lines is the point that satisfies and
. It is the solution to
 -->  -->  -->  and
with  -->  -->  -->  -->  .
That intersection is the point C(2,3).
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