Develop an appropriate model for the following business decision scenario, and use that model to determine the optimal decision alternative. In designing a new space vehicle, NASA needs to decide – based on expected cost – whether to provide 0, 1, or 2 backup systems for a critical component of the vehicle. The first backup system, if included, comes into use only if the original system fails, and the second backup system, if included, would only come into use if both the original system and the first backup system fail. NASA engineers have estimated that each system, independently of the others, has a 1% probability of failing when/if put to use. The incremental cost in building the vehicle will be $70,000 for each backup system included; otherwise, the basic cost of the vehicle does not need to be considered in the decision process. Once the space vehicle is deployed on its mission, the mission will have to be aborted if the original system and all backup systems fail. The estimated cost for aborting the mission is $8,000,000 (not including any incremental backup system cost).