A long time ago in a galaxy far, far away. In order to control the galaxy, The E

Question

A long time ago in a galaxy far, far away. In order to control the galaxy, The Empire's spaceships need to be able to reach any point in the galaxy within 24 hours. There are two types of spaceships available: space cruisers (speed 0.1 astronomical units per hour; building price 1,000 credits) and more advanced battleships (speed 0.4 astronomical units per hour; building price 50,000 credits). The whole galaxy can be taken under control with 6400 space cruisers. How many battleships are needed in order to do this? The Empire is just starting to build the space fleet in order to take the galaxy under control. What is cheaper, to build only space cruisers or only battleships and why? The price of printing a 4" times 6" photo is $0.15. Assuming that the price depends on ink consumption, what is the fair price to print a 8" times 12" photo?

Explanation / Answer

To take whole galaxy under control, 6400 cruisers are needed which each travel at a speed of 0.1 au per hour

So, battleships at speed of 0.4 au per hour required will be = 6400 * (0.1/0.4) = 1600 battleships

For 6400 cruisers credits needed = 6400 * 1000 = 6400000

For 1600 battleships credits needed = 1600 * 50000 = 80000000

So, they should produce only cruisers as these cost less credits.

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