Linear Inequalities

Concept:Formulating linear inequality constraints for resource allocation.Explanation:Let $x$ = number of bags of Grade I fertilizer and $y$ = number of bags of Grade II fertilizer.Plant A constraint: $6$ hrs per bag of Grade I and $3$ hrs per bag of Grade II, maximum $120$ hrs → $6x + 3y \leq 120$.Plant B constraint: $4$ hrs per bag of Grade I and $10$ hrs per bag of Grade II, maximum $180$ hrs → $4x + 10y \leq 180$.All constraints are non-strict inequalities (≤) because the usage cannot exceed the available time.Answer:The correct mathematical representation is $6x + 3y \leq 120$ and $4x + 10y \leq 180$, which corresponds to option C.