Question

A research laboratory is formulating a daily dosage protocol for a clinical trial combining two therapeutics, Drug A ($A$) and Drug B ($B$), measured in integer milligrams (mg).

The trial protocol specifies the following operational constraints:
- The daily dosage of Drug A must be at least $10\text{ mg}$ and at most $40\text{ mg}$ ($10 \leq A \leq 40$).
- The daily dosage of Drug B must be at least $15\text{ mg}$ and at most $50\text{ mg}$ ($15 \leq B \leq 50$).
- To prevent hepatotoxicity, the combined daily dosage $(A + B)$ cannot exceed $65\text{ mg}$ ($A + B \leq 65$).
- To ensure therapeutic efficacy, the dosage of Drug B must be at least $10\text{ mg}$ less than twice the dosage of Drug A ($B \geq 2A - 10$).

The total treatment efficacy score $E$ is modeled by the linear function $E = 3A + 4B$.

Based on the constraints above, select the daily dosage for Drug A and the daily dosage for Drug B that together maximize the total treatment efficacy score $E$.