Question 5 has more but can't add it here so just request it when you need it. Thanks

Minimize z = 4x1 + x2 subject to 3x1 + x2 = 3 4x1 + 3x2 6 x1 + 2x2 4 X1, X20 Use the Big M method, with M = 100, to construct the complete first simplex tableau for the simplex method and identify the corresponding initial basic feasible solution. Also identify the initial entering non- basic variable and the leaving basic variable. 4. Consider the following LP problem. [11] Maximize z = -2x - x2 + x3 subject to x1 + x2 + x3 3 x2 + x3 2 x1 +x3 = 1 X1, X2, X30 (i) Find the dual of this LP problem. (ii) [5] After adding a slack variable s, subtracting an excess variable e2, and adding artificial variables a and a3, Row 0 of the LP problem's optimal tableau is found to be z = 4x1 + 2 + (M 1)a+ (M + 2)a3 = 0 Find the optimal solution to the dual of this LP problem. [3] 5. Consider the following problem. Maximize z = 3x + 2x2 subject to 2x1 + x2 100 x1 + x2 80 1 40 X1, X20 In the problem x = toy soldiers and x2 = toy trains. The objective function is the profit made from the manufacture and sale of the toy soldiers and toy trains. So, toy soldiers contribute $3 to profit and toy trains contribute $2 to profit.