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- Write algorithm for the continually growing set of linear approximations of the constraints simply makes a better and better outer approximation of the original nonlinear constraints.(b) The Double SAT problem asks whether a given satisfiability problem has at least two different satisfying assignments. For example, the problem {{V1, V2}, {V1, V2}, {V1, V2}} is satisfiable, but has only one solution (v₁ = F, v₂ = T). In contrast, {{V1, V2}, {V1, V2}} has exactly two solutions. Show that Double-SAT is NP-hard.Why is it absolutely necessary, while attempting to solve issues involving linear programming, to give the object function a larger weight than the constraints?
- Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. Use linear programming methods to solve this problem. Represent the constraints and the objective function mathematically in code. Use Python and the SciPy and Matplotlib libraries to solve the problem and visualize the optimal solution on a graph. Clearly state the optimal solution and any assumptions made while solving the problem. A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows: - Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram. The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber.…Given a square matrix A of dimension n, which has only non-null elements in the inputs Aj1, Aji, Aji+1, An1 and Ann for all i e {1,2, ., n – 1} Make a function that solves a system A, = b by the Jacobi method that uses of A and receives as parameters the Inputs: A; b; The starting point; The maximum required tolerance; Maximum number of iterations. (Octave/ Matlab) the structure Explain the steps pls.(a) Stingy SAT is the following problem: given a set of clauses (each a disjunction of literals) and an integer k, find a satisfying assignment in which at most k variables are true, if such an assignment exists. Prove that stingy SAT is NP-hard. (b) The Double SAT problem asks whether a given satisfiability problem has at least two different satisfying assignments. For example, the problem {{V1, V2}, {V1, V2}, {V1, V2}} is satisfiable, but has only one solution (v₁ = F, v₂ = T). In contrast, {{V1, V2}, {V1, V2}} has exactly two solutions. Show that Double-SAT is NP-hard.
- Why is it so important that in linear programming problems the object function be given greater weight than the constraints?Construct a PYTHON program code for an inequality constraint minimization via logarithm barrier method.(OPTIMIZATION) For this problem minimize –x + /y subject to (x – 5)² + (y – 3)² < 3/2 x < 5 -If the objective function is concave and the constraints are linear, the Solver is guaranteed to discover the global minimum (if one exists). Is it true or false?
- Detecting Type-B Arbitrage with (ADLP) - Practice For type-B arbitrage the following conditions neèd to be satisfied: Po(y) = E söx; s0, (i) i=0 ES{(w; )x; > 0, j = 1, 2, ..., m, (ii) i=0 in Es{(w;)x; > 0 for at least one index j (ii) i=0 We can find such an investment x (if one exists) by solving ОРТ min - j=1 i=0 subject to S;(w;)x; > 0, j = 1, 2, . . . , m. (ADLP) i=0 in Sóx; <0 i=0 Define OPT = -o if the problem is unboundedGenerate the Simulink models for the constitutive equations of stress and strain for Kelvin-Voigt and Maxwell viscoelastic models with the following constraints: Your source should always be a step function with a step of 10 - regardless of whether it's stress or strain For all models, use the following values: E-3 n-5 You should have a total of 4 models: 1. Kelvin Voigt– input is strain, output (scope) is stress 2. Kelvin Voigt – input is stress, output (scope) is strain 3. Maxwell – input is strain, output (scope) is stress 4. Maxwell – input is stress, output (scope) is strainFill in only five of the following with a short answer 1. It can assign solution type (minimum or maximum) of control problem through 2. The function of integral control is 3. The system is in critial stable if 4. A third order system with an output equation (y = 2x₁ - x₂) its output matrix is_ 5. A system with state matrix A = [¹ 2] its overshoot value is 6. The stability of the open-loop system depandes on