please answer the questions below

Example 5.3.1. Consider the linear programming problem of Maximizing z = 11x1 +4x2 +x3 + 15x4 (5.3.1) subject to 3x1+ 12+2JC3+4I4528 8x1+2x2 x3+7x4550 xl,xg,13,x4 2 0 Adding slack variables and then applying the simplex algorithm yields the reduced tableaux resolution shown in Table 5.5. The maximum value of z is 106. attained at the point (0,4,0,6). Table 5.5 Q3 (2 points) Section 5.4 #1 (c) Solve the problem of (5.3.1) from Section 5.3 starting from the second tableau in Table 5.5 if a variable x7 2 0 is added to the problem with the given specifications in part (c). Problem Set 5.4 1. Solve the problem of (5.3.1) of Section 5.3. starting from the second tableau of Table 5.5, if a variable x-; 2 0 is added to the problem as stated in (5.3.1). with: (c) A\") = [6;ll]'. coefficient ofx1 in z = 15 Q4 (2 points) Section 5.5 #2 (a) References Example 3.5.1 on page 87. Determine the max value of the objective function and a point at which this value is attained if we make the specied change. 2. Consider the linear programming problem of Example 3.5.1 on page 87. De- termine the maximum value of the objective function and a point at which this value is attained if (a) b; is increased from 10 to 30 units, bl and b3 remaining unchanged. 05 (2 points) Practice using the Dual Simplex Algorithm. Using the second frame of Table 5.5. find the optimal value of the objective function and a point at which the value is attained if b = [28, 50]T in the problem of (5.3.1) of Section 5.3 is changed to [29, 50]T