1 Assignment 3 due on Nov.13 Problem 1: 50 pts Work through the simplex method (in algebraic form) step by step to solve the following problem.

1Assignment 3 due on Nov.13Problem 1: 50 ptsWork through the simplex method (in algebraic form) step by step to solve the followingproblem.Maximize Z = x1 + 2x2 + 2x3,subject to5x1 + 2x2 + 3x3 ≤ 15x1 + 4x2 + 2x3 ≤ 122x1 + x3 ≤ 8andx1 ≥ 0, x2 ≥ 0, x3 ≥ 0.Problem 3:Consider the following problem.Minimize Z = 3x1 + 2x2,subject to2x1 + x2 ≥ 10-3x1 + 2x2 ≤ 6x1 + x2 ≥ 6andx1 ≥ 0, x2 ≥ 0.(a) Solve this problem graphically. 10 pts(b) Using the Big M method, construct the complete first simplex tableau for the simplexmethod and identify the corresponding initial (artificial) BF solution. Also identify theinitial entering basic variable and the leaving basic variable. 20 pts(c) Work through the simplex method step by step to solve the problem. 20 pts