If the constraint is defined as 3D + 2W ≤ 18, what is the maximum value of D?

To find the maximum value of ( D ) in the constraint ( 3D + 2W \leq 18 ), we can first isolate ( D ). Rearranging the equation gives us:

[ 3D \leq 18 - 2W ]

Now, dividing every term by 3 yields:

[ D \leq 6 - \frac{2}{3}W ]

From this inequality, it is clear that ( D ) is dependent on the value of ( W ). To maximize ( D ), we must minimize the term ( -\frac{2}{3}W ). The smallest possible value of ( W ) is 0 (assuming ( W ) cannot be negative), leading us to:

[ D \leq 6 - 0 \implies D \leq 6 ]

Therefore, the maximum possible value for ( D ) is 6. This means if ( W = 0 ), then ( D ) reaches its maximum value of 6 while still satisfying the constraint ( 3D + 2W \leq 18 ).

Consequently, among the options provided,