Algorithm OPTIMAL-PARAMETRIZATION. Given F(x, y, z) ∈ Q[x, y, z], an irreducible homogeneous polynomial defining a rational plane curve C, the algorithm computes an optimal rational parametrization of C

W1 a W2 w6 w7 6. -1 4 W3 W5 e W4 Figure 1: Weighted, undirected graph G. Weights and Source Node All problems use weights wi through w7. To determine these weights, look at your 7 digit ID. The weight wi corresponds to the first digit of your ID, the weight w2 corresponds to the second digit of your ID, and so on. For problems 2 and 4, we use a source node or starting node s, determined as follows: find the digit in your ID that has the highest value. If it is the first digit then s = a, if it is the second digit, then s = b, and so on. If there is more than one digit with the same highest value, choose the first occurrence of that digit. For example, if your ID is 4526767, then the highest value is 7, and you choose the first 7, i.e., digit 5, and set s = е.

Write all the three properties of shortest path and generic algorithm for solving a single source shortest path problem.

Any linear program L, given in standard form, either1. has an optimal solution with a finite objective value,2. is infeasible, or3. is unbounded.If L is infeasible, SIMPLEX returns “infeasible.” If L is unbounded, SIMPLEXreturns “unbounded.” Otherwise, SIMPLEX returns an optimal solution with a finiteobjective value.

Any linear program L, given in standard form, either1. has an optimal solution with a finite objective value,2. is infeasible, or3. is unbounded.If L is infeasible, SIMPLEX returns “infeasible.” If L is unbounded, SIMPLEXreturns “unbounded.” Otherwise, SIMPLEX returns an optimal solution with a finiteobjective value.

Problem: Solve the following equality-constrained optimiza- tion problem using Newton descent algorithm with the initial point (1, 4, 0): min f(x, y, z) = e" + 2y? + 3z2 x,y,z subject to x – 5z = 1 | y + z = 4 Compute the optimal dual variables as well. You have to answered above problem By using Python Programming Language.

I only need part B in the image, I have already completed part A. How do I formally prove that by using consecutive powers for the values of coins, that it will give me the optimal solution? (using induction preferably unless an easier formal proof is available)