a Problem 2. Suppose we are trying to solve the following LP. maximize 21 +2+2 +3.03 subject to 21 +02 > 2 2.01 +32 +33 0 (a) [3pt) We will use the simplex method to solve this LP, by converting this LP to a standard form, and then introducing two slack variables 24,15. Write down the augmented form of LP. (b) (2pt] To apply simplex method, as the preparation step, we need to find a feasible initial point. For this problem, since the origin is not a feasible solution, instead of the origin we start from a feasible solution that satisfies 31 = 0, 12 = 2, 13 = 0,24 = 0,15 = 2. If you directly write down a tableau based on these values (let's call it a "naive tableau"), then it is not a simplex tableau since it does not satisfy the properties of a simplex tableau. The naive tableau is provided as the following. Basic Var. Z 21 22 23 24 25 RHS Z -1 -2 -3 0 0 22 1 1 0 -1 0 2 0 2 1 1 0 1 4 Which properties (or property) do(es) the naive tableau violate? Explain. (c) [3pt] Please create a simplex tableau, i.e., a tableau which satisfies the required properties of a simplex tableau, by certain operations (i.e., transform the naive tableau into a simplex tableau). Remark: Some values of the desired simplex tableau after the transformation (not the naive tableau) are already given below. Basic Var. 23 24 25 RHS Z ? ? ? ? ? ? 22 ? ? ? ? ? ? 2 T5| ? ? ? ? ? ? 2 0 1 0 15 Z 21 22 No.10.10