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1. An aerospace engineering design and manufacturing company produces two systems to address the needs of their market niche. Both systems require the same two main processes performed at different assembly lines. Process 1 is usually completed in 3 days for System 1 and in 5 days for System 2. The second process (Process 2) requires 6 days for System 1 and 9 days for System 2. The company has 25 days available for Process 1 and 40 days available for Process 2. System 1 is sold for $200, while System 2 is sold for $350. Formulate the problem as a linear programing model (Solving the model is not required). 2. An air transportation company plans an expansion to its current operations. The plan includes shipping cargo from city A to city B with a maximum cargo level of 10 tons. There are four different items that can be shipped with their information presented in the table. Each item has a weight in tons, can make a profit in thousands of dollars, and it is limited in terms of current supply (availability for shipping). If an item is selected, then all number available for shipping for that particular item will be shipped. Item (i) Weight (wi) Profit/Unit (pi) Number available (ni) 1 1 3 6 2 4 9 1 3 3 8 2 4 2 5 2 Let Xi = 1 if object i is selected and 0 otherwise. Then the vector represents a solution of the problem. The solution is feasible only if 1-1 Winixi W, where W = 10. For example, weight constraint for chromosome (1 100) is W = winl + w2n2 = (1)(6)+(4)(1)=10. The fitness for chromosome (x1 x2 x4) is F = Citilinixi. For example, fitness for chromosome (1 1 0 0) is F = pini + p2n2 = (3)(6)+(9)(1)=27 with W = 10. Start with the initial population: P1 = (1 100) and P2 = (0011) Develop an evolutionary approach to search for the optimum solution for this problem. Use crossover, inversion, or mutation operators. Stop the search when you first obtain an improved solution.

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