Question

a) Change the right-hand-side value of one of the constraints. Be sure that, the updated
tableau is infeasible, and you are applying Dual Simplex Method. (Find a change that will
make the new tableau infeasible.)
b) Change the objective function coefficient of one of the decision variables. Be sure that,
the updated tableau is non-optimal, and you are applying Simplex Method. (Find a
change that will make the new tableau non-optimal.)
c) Find the validity range for one of the constraint’s right-hand-side value.
d) Find the optimality range for one of the decision variable’s objective function coefficient.
e) Add a new ≥ constraint into the model. Be sure that, the new constraint is not satisfied by
the current optimal solution and you are applying Dual Simplex Method. (Add a ≥
constraint that will make the new tableau infeasible.)
f) Add a new decision variable into the model. Be sure that, the new tableau is non-optimal,
and you are applying Simplex Method. (Add a new decision variable that will make the
new tableau non-optimal.)

Answer 1

a)In the tableau implementation of the primal simplex algorithm, the right-hand-side column is always nonnegative so the basic solution is feasible at every iteration

Alternatively, when some of the elements are negative, we say that the basis is primal infeasible. Up to this point we have always been concerned with primal feasible bases.

With reference to the tableau, the algorithm must begin with a basic solution that is dual feasible so all the elements of row 0 must be nonnnegative. The iterative step of the primal simplex algorithm first selects a variable to enter the basis and then finds the variable that must leave so that primal feasibility is maintained. The dual simplex method does the opposite; it first selects a variable to leave the basis and then finds the variable that must enter the basis to maintain dual feasibility. This is the principal difference between the two methods. The algorithm below assumes a basic solution is described by a tableau.

b)Change the objective function coefficient of one of the decision variables. Be sure that,
the updated tableau is non-optimal, and you are applying Simplex Method. (Find a
change that will make the new tableau non-optimal.

Clearly, if the contribution is reduced from $6 per case to something less it would certainly not become attractive to produce champagne glasses. If it is now not attractive to produce champagne glasses, then reducing the contribution from their production only makes it less attractive. However, if the contribution from production of champagne glasses is increased, presumably there is some level of contribution such that it becomes attractive to produce them.

c)The range of feasibility is the range over which the shadow price is applicable. As the RHS increases, other constraints will become binding and limit the changes in the value of the objective function.

d)Graphically, the limits of a range of optimality are found by changing the slope of the

objective function line within the limits of the slopes of the binding constraint lines

 Slope of an objective function line, Max c1x1+ c2x2, is -c1/c2, and the slope of aconstraint, a1x1+ a2x2= b, is -a1/a2