Calculate the amphotericin infusion dose, volume, and rate for a patient weighing 89 kg, prescribed 250 µg/kg, with a maximum concentration of 200 µg/mL, to be infused over 2.5 hours.

$$\text{Total dose} = 22250\text{ }\mu\text{g} \times \frac{1\text{ mg}}{1000\text{ }\mu\text{g}} = 22.25\text{ mg}$$

The dose of amphotericin required by the patient is $\boxed{\textbf{22.25 mg}}$.

2. Calculate the volume of IV solution required by the patient if the solution contains the maximum concentration.

$$\text{Volume} = \frac{\text{Total dose}}{\text{Concentration}} = \frac{22250\text{ }\mu\text{g}}{200 \frac{\mu\text{g}}{\text{mL}}}$$ $$\text{Volume} = 111.25\text{ mL}$$

The volume of IV solution required by the patient is $\boxed{\textbf{111.25 mL}}$.

3. If the solution has to be delivered in 2.5 hours, what is the rate in mL/minute?

$$\text{Rate} = \frac{\text{Volume}}{\text{Time}} = \frac{111.25\text{ mL}}{150\text{ min}}$$ $$\text{Rate} \approx 0.7417 \frac{\text{mL}}{\text{min}}$$

The rate of infusion is approximately $\boxed{\textbf{0.74 mL/minute}}$.

4. If a 50mg vial is used to prepare the IV solution, what is the total volume of the solution prepared?

$$\text{Total volume} = \frac{\text{Amount of drug}}{\text{Concentration}} = \frac{50000\text{ }\mu\text{g}}{200 \frac{\mu\text{g}}{\text{mL}}}$$ $$\text{Total volume} = 250\text{ mL}$$

The total volume of the solution prepared from a 50mg vial at the maximum concentration is $\boxed{\textbf{250 mL}}$.