As you should know at this point, the United Federation of Planets has an ongoing mission of discovering new worlds, to seek out new lifeforms and new civilizations, to boldly go where no one has gone before.

However, due to a shortage of dilithium, Starfleet Command has grounded the fleet. We must launch our ships using conventional old chemical rockets from the 21st Century.

You are the Chief Engineer on duty today. You have access to a 3-stage heavy launch vehicle with a Total Launch Mass of 65,000,000 kg (limited by the structural integrity of the launch pad).

Based on the engines efficiency and Delta V requirements, your science officer Spock has already calculated the payload ratios (lambda) for each stage as follows:

• Stage 3 (Final stage): λ_3 = 0.281

• Stage 2 (Intermediate): λ_2 = 0.238

• Stage 1 (Liftoff): λ_1 = 0.155

Task: Calculate the maximum payload capacity of this vehicle. Based on your result, which ship can you successfully deliver to a space injection trajectory?

- USS Enterprise, Constitution class, 1 million kg.

- USS Voyager, Intrepid class, 510,000 kg

- USS Defiant, Defiant class, 355,000 kg