(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.

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.…

Demonstrate that the following issue falls within the NP class: A set S of integers and an integer number t are provided to us. Exists a subset of S such that the product of its components equals t? Note: Problem with Data Structures and Algorithms

2. Consider the language DOUBLE-SAT, all of the boolean expressions with at least two satisfying assignments. (a) What would a possible DOULBE-SAT solution look like for an expression? (b) Is DOUBLE-SAT in NP?