Optimization — Base Cylinder Compounding

To minimize the total number of measurements needed to reach exactly 298 liters, apply a standard mathematical greedy approach, selecting the largest possible volumetric measures sequentially.

Let us check if a non-greedy allocation yields fewer steps by overshooting: 3 × 100 = 300 liters. To get back to 298, we would need to remove 2 liters, but since we are drawing water from a tank with standard cylinders, we can only add positive measurements to aggregate the total volume. Alternatively, using four 25L components instead of a 100L container increases our count. Let's look closely at the math for another configuration: 2 × 100 + 4 × 25 = 300 (exceeds). Let's review 2 × 100 + 3 × 25 + 3 × 6 + 5 × 1 = 13. Let's check if we can optimize using 298 = 200 + 100 - 2 (cannot subtract). Is there a combination like 2 × 100 + 3 × 25 + 4 × 6 - 1 × 1 = 13? Let's re-verify the baseline math. If we pick 298 = 2 × 100 + 3 × 25 + 3 × 6 + 5 × 1 = 13 steps. Let's test alternative groupings: 2 × 100 + 4 × 25 = 300 (cannot do). Can we use 298 = 2 × 100 + 3 × 25 + 4 × 6 = 299 (close, but need 1L residual adjustment). The exact step distribution corresponds to 2 + 3 + 3 + 5 = 13.

Answer: (d).