please show every step and write everything very clear

Consider the following LP: maxz=s.t.3x1+2x22x1+x2100x1+x280x140x1,x20 In order to bring the problem into standard form, we have to add the slack variables s1,s2 and s3. The optimal tableau is given in the following table: (a) Show that as long as the objective function coefficient of variable x1 is between 2 and 4 , the current basis remains optimal. Find the optimal solution if the objective function coefficient of variable x1 has value 3.5. (b) Show that as long as the objective function coefficient of variable x2 is between 1.5 and 3 , the current basis remains optimal. (c) Show that if the RHS of the first constraint varies between 80 and 120, then the current basis remains optimal. Find the new optimal solution if the RHS of the first constraint changes to 90 . Consider the following LP: maxz=s.t.3x1+2x22x1+x2100x1+x280x140x1,x20 In order to bring the problem into standard form, we have to add the slack variables s1,s2 and s3. The optimal tableau is given in the following table: (a) Show that as long as the objective function coefficient of variable x1 is between 2 and 4 , the current basis remains optimal. Find the optimal solution if the objective function coefficient of variable x1 has value 3.5. (b) Show that as long as the objective function coefficient of variable x2 is between 1.5 and 3 , the current basis remains optimal. (c) Show that if the RHS of the first constraint varies between 80 and 120, then the current basis remains optimal. Find the new optimal solution if the RHS of the first constraint changes to 90