The design of a system is to be chosen from two design alternatives. The system will have a life of 12 years. Each design alternative has a life-cycle cost associated with an expected future. The tables below give the life-cycle cost (in millions of dollars) for Design 1 for the 3 possible futures F1, F2, and F3; and the life-cycle cost (in illions of dollars) for Design 2 for the 3 possible futures F1, F2, and F3. The probability of occurrence for F1-30%; the probability of occurrence for F2-50%; and the probability of occurrence for F3- 20%. Use an interest rate of 10% Design Year 1 Year 2 Year 3 Year4 Year 5 Year 6 Year7 Year8 Year 9Year 10 Year 11 Year 12 Cost tCost Cost Cost Cost 0.4 0.6 0.8 CostCostCost 0.8 Cost Cost Cost 0.8 Cost 0.8 0.6 0.8 0.9 0.8 0.8 0.8 0.8 0.8 F2 F3 1.2 1.2 1.2 1.2 1.2 Design Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year7 Year8 Year 9Year 10 Year 11 Year 12 Cost Cost 0.4 0.8 0.8 Cost Cost F1 F2 F3 Cost 2.5 3.0 Cost 2.5 3.0 Cost 2.5 3.0 3.1 Cost otCost 2.5 3.0 0.4 2.5 3.0 2.5 3.0 2.5 0.6 0.6 a) Which design alternative is most desirable from an expected cost viewpoint? b) Which design alternative is most desirable using the Laplace Criterion