​ What constraints are placed on the variables in this situation?

x  =  number of round tables     and     y  =  number of rectangular tables

 

Each round table has 6 chairs. Each rectangular table has  10  chairs.

The total number of chairs must be greater than or equal to  185  .

 

6x + 10y  ≥  185

 

There must be no more than  15  rectangular tables.

So the number of rectangular tables must be less than or equal to  15 .

 

y  ≤  15

 

There must be no fewer than  6  round tables.

So the number of round tables must be greater than or equal to  6 .

 

x  ≥  6

 

The number of rectangular tables must be greater than or equal to one-third the number of round tables.

y  ≥  \(\frac13\)x

3y  ≥  x

 

x  ≤  3y