$1.$ Choose a Real$-$World Problem:o Select a problem relevant to optimization $($e$.$g$.,$ resource allocation, scheduling,or minimization of costs in some process$).$o The problem must include constraints and objectives that can be formalized intoa standard optimization problem $($i$.$e$.,$ objective function, constraints, andvariables$)\mathrm{.}2.$ Standard Problem Formulation:o Clearly define the decision variables, constraints, and objective function in mathematical form.o The problem should be expressed in a form that allows solving with both exact and approximate methods $($e$.$g$.,$ linear programming, integer programming, or non$-$linear programming$).$Deliverables for Part $1$: A report section detailing the problem and how it has been mathematically formulated. Explanation of the relevance and importance of the problem to a real$-$world scenario.Part $2$: Optimization Methods Implementation$1.$ Implement Exact Optimization Methods:o Implement an exact method $($e$.$g$.,$ Integer Linear Programming, gradientdescent, simplex method, branch$-$and$-$bound, etc.$)$ to solve the problem.o Test and validate the performance of the method on the formulated problem$\mathrm{.}2.$ Implement Approximate Optimization Methods:o Implement at least one approximate method $($e$.$g$.,$ simulated annealing, geneticalgorithms, or particle swarm optimization$).$o Test and compare the performance of the approximate method against the exactmethod in terms of solution quality, computational efficiency, and robustness. $3.$ Comparison and Analysis:o Compare the results obtained from exact and approximate methods in terms of optimality, time complexity, and practical usability.o Analyze the performance of the methods in different scenarios $($e$.$g$.,$ different constraint sets or input data variations$).$o Discuss under what conditions each method is preferable. Deliverables for Part $2$: Code implementations for both exact and approximate methods. A detailed report section that:o Explains the methodology behind each algorithm.o Includes a comparison between the results obtained from different methods. o Offers insight into the effectiveness of the methods.