how do you solve this question?

Suppose the government wants to hire a space ight rm to bring a rock from the Moon back to Earth, so it offers a $1 billion contract. Two rms, Blue Origin (Firm B) and SpaceX (Firm S), want to win this contract. The government will award the contract to whichever rm promises to bring the Moon rock back sooner. If both rms promise to bring the Moon rock back at the same time, the government will randomize over which one to select for the contract, and so award the contract to Firm B or to Firm S each with probability 5 Before the competition starts, the rms must simultaneously decide how quickly to promise to bring the Moon rock back. Firm is promise is t, > 0, the time it will take to obtain the Moon rock, measured in years. (The rm's promise It,- may be any positive real number.) The cost of bringing back the Moon rock in t,- years is _ $1 billion _ t, C(ti) If rm i is awarded the contract, it will have to incur the cost to bring back the Moon rock at the time that it promised, and its prot will be $1 billion C(ti). If rm i is not awarded the contract, it will earn zero prot. Each rm wants to maximize its expected prot. i) 15 points: If the other rm will promise t_,- > 1, what are rm is best responses? ii) 15 points: If the other rm will promise t_,-