You Have $1 Billion To Win A Space Race. Go.

Problem

You are the CEO of a space transport company in the year 2080, and your chief scientist comes in to tell you that one of your space probes has detected an alien artifact at the Jupiter Solar Lagrangian (L2) point.

You want to be the first to get to it! But you know that the story will leak soon and you only have a short time to make critical decisions. With standard technology available to anyone with a few billion dollars, a manned rocket can be quickly assembled and arrive at the artifact in 1,600 days. But with some nonstandard items you can reduce that time and beat the competition. Your accountants tell you that they can get you an immediate line of credit of $ $1$ billion.

You can buy:

Big Russian engines. There are only three in the world and the Russians want $ $400$ million for each of them. Buying one will reduce the trip time by $200$ days. Buying two will allow you to split your payload and will save another 100 days. NASA ion engines. There are only eight of these $ $140$ million large-scale engines in the world. Each will consume $5,000$ kilograms of xenon during the trip. There are $30,000$ kg of xenon available worldwide at a price of $ $2,000$/kg, so $5,000$ kg costs $ $10$ million. Bottom line: For each $ $150$ million fully fueled xenon engine you buy, you can take 50 days off of the trip. Light payloads. For $ $50$ million each, you can send one of four return flight fuel tanks out ahead of the mission, using existing technology. Each time you do this, you lighten the main mission and reduce the arrival time by $25$ days. What’s your best strategy to get there first?

Solution

from itertools import product

#Number available
num_re = 3
num_ie = 8
num_ft = 4
num_xe = 6 #30000/5000 

#Costs in millions
re_cost = 400
ie_cost = 140
ft_cost = 50
xe_cost = 10

#Savings in days
ie_saving = 50
ft_saving = 25
re_saving = {0:0, 1:200, 2:300, 3:500}

#Available loan
loan = 1000

optimal_sols =[]
for r, i, f, x in product(range(num_re+1), range(num_ie+1), 
                            range(num_ft+1),  range(num_xe+1)):
    days_saved = f*ft_saving + min(x, i)*ie_saving + re_saving[r]
    total_cost = f*ft_cost + i*ie_cost + r*re_cost + x*xe_cost
    days_savings_avlbl = (num_ft-f)*ft_saving + \
        min(num_ie-i, num_xe-x)*ie_saving + re_saving[num_re-r] 
    if total_cost <= loan and days_saved > days_savings_avlbl:
        optimal_sols.append((days_savings_avlbl, days_saved, r, i, f, x))

for dsa, ds, r, i, f , x in optimal_sols:
    print("Number of Russian Engines: ", r)
    print("Number of Ion Engines: ", i)
    print("Number of Fuel Tanks: ", f)
    print("Number of Xenon kgs: ", x*5000)
    print("Total number of days saved: ", ds)
    print("Total day savings available: ", dsa)
    print("\n")

Valid combinations

Number of Russian Engines: 1

Number of Ion Engines: 1

Number of Fuel Tanks: 4

Number of Xenon kgs: 30000

Total number of days saved: 350

Total day savings available: 300

Number of Russian Engines: 1

Number of Ion Engines: 2

Number of Fuel Tanks: 3

Number of Xenon kgs: 30000

Total number of days saved: 375

Total day savings available: 325

Number of Russian Engines: 1

Number of Ion Engines: 2

Number of Fuel Tanks: 4

Number of Xenon kgs: 25000

Total number of days saved: 400

Total day savings available: 350

Number of Russian Engines: 1

Number of Ion Engines: 2

Number of Fuel Tanks: 4

Number of Xenon kgs: 30000

Total number of days saved: 400

Total day savings available: 300

Number of Russian Engines: 1

Number of Ion Engines: 3

Number of Fuel Tanks: 2

Number of Xenon kgs: 30000

Total number of days saved: 400

Total day savings available: 350

Number of Russian Engines: 2

Number of Ion Engines: 0

Number of Fuel Tanks: 1

Number of Xenon kgs: 30000

Total number of days saved: 325

Total day savings available: 275

Number of Russian Engines: 2

Number of Ion Engines: 0

Number of Fuel Tanks: 2

Number of Xenon kgs: 25000

Total number of days saved: 350

Total day savings available: 300

Number of Russian Engines: 2

Number of Ion Engines: 0

Number of Fuel Tanks: 2

Number of Xenon kgs: 30000

Total number of days saved: 350

Total day savings available: 250

Number of Russian Engines: 2

Number of Ion Engines: 0

Number of Fuel Tanks: 3

Number of Xenon kgs: 20000

Total number of days saved: 375

Total day savings available: 325

Number of Russian Engines: 2

Number of Ion Engines: 0

Number of Fuel Tanks: 3

Number of Xenon kgs: 25000

Total number of days saved: 375

Total day savings available: 275

Number of Russian Engines: 2

Number of Ion Engines: 1

Number of Fuel Tanks: 0

Number of Xenon kgs: 30000

Total number of days saved: 350

Total day savings available: 300