Give a) an example of a valid instance of the summation problem that is not a valid instance of the minimum problem, and b) vice-versa. Write the problem definition for each of these problems.

Please do the following questions with the full python coding and explanation below each question typed

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.…

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.