How can an optimisation problem be represented mathematically. Explain with the help of an example. Explain the steps of designing a Greedy solution for an optimisation problem. Also explain the concept of local and global optimal solutions. Solve the following fractional Knapsack problem using greedy approach. Show all the steps.
An optimization problem can be represented mathematically by defining an objective function, a set of decision variables, and a set of constraints. The decision variables represent the choices to be made, the objective function represents the quantity to be maximized or minimized, and the constraints restrict the feasible values of the decision variables. In general form, an optimization problem can be written as: maximize or minimize f(x), subject to gᵢ(x) ≤ bᵢ for i = 1, 2, …, m, where x = (x₁, x₂, …, xₙ) are the decision variables, f(x) is the _____ ___ _____ ___ ______ ___.
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Figure 1: A sample weighted Grари
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How can an optimisation problem be represented mathematically. Explain with the help of an example. Explain the steps of designing a Greedy solution for an optimisation problem. Also explain the concept of local and global optimal solutions. Solve the following fractional Knapsack problem using greedy approach. Show all the steps.