SOLUTION: Hi! A man and his daughter manufacture unfinished tables and chairs. Each table requires 2 hours of sawing and 2 hours of assembly. Each chair requires 1 hour of sawing and 3 ho

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi! A man and his daughter manufacture unfinished tables and chairs. Each table requires 2 hours of sawing and 2 hours of assembly. Each chair requires 1 hour of sawing and 3 ho      Log On


   

Question 200312: Hi!
A man and his daughter manufacture unfinished tables and chairs. Each table requires 2 hours of sawing and 2 hours of assembly. Each chair requires 1 hour of sawing and 3 hours of assembly. The two of them can put in up to 10 hours of sawing and 12 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. (Assume x is the number of tables and y is the number of chairs.)
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Sawing criteria: . That is the time spent sawing to make tables plus the time spent sawing to make chairs must be less than or equal to the total amount of time available for sawing.

Assembly criteria: . That is the time spent assembling tables plus the time spent assembling chairs must be less than or equal to the total amount of time available for assembly.

Non-negative criteria: and . You can't make a negative amount of either chairs or tables.

You might also want to restrict the solution for this problem to the integers. Making half a table doesn't seem to make much practical sense. And one of the critical points which may end up being an optimum based on how you define your objective function is the intersection of the two labor resource criterion inequalities, specifically the point (4.5,1). This would suggest that a potential optimum solution could, in fact, be making 4 and a half tables.



You need to shade the feasible area, namely that area bounded by the green line on top, the red line on the right, and the two coordinate axes.


John