The dual of the primal maximization LP problem having m constraints and n non-negative variables should:
Have n constraints and m non-negative variables
Be a minimization LP problem
Both 1 and 2
None of the above
For any primal problem and its dual,
Optimal value of objective functions is same
Primal will have an optimal solution if and only dual does too
Both primal and dual cannot be infeasible
All of the above
The right hand side constant of a constraint in a primal problem appears in the corresponding dual as
A coefficient in the objective function
A right hand side constant of a constraint
An input- out coefficient
None of the above
Dual LP problem approach attempts to optimize resource allocation by ensuring that
Marginal opportunity cost of a resource equals its marginal return
Marginal opportunity cost of a resource is less than its marginal return
Both a and b
None of the above
Shadow price indicates how much one unit change in the resource value will change the
Optimality range of an objective function
Optimal value of the objective function
Value of the basic variable in the optimal solution
None of the above
Principle of complementary slackness states that
Primal slack x dual main = 0
Primal main x dual surplus = 0
Both 1 and 2
None of the above
If dual has an unbounded solution, primal has
No feasible solution
Unbounded solution
Feasible solution
None of the above
If at the optimality a primal constraint has positive value of slack variable, then
Dual variable corresponding to that constraint has zero value
Corresponding resource is not completely used up
Corresponding resource have zero opportunity cost
Both 2 and 3 but not 1
The shadow price is
The price that is paid for purchase of resource
The saving by elimination one of the excess quantities of resource
The increase in the objective function value by providing one additional unit of resource
None of the above
The value of dual variable
Represents marginal profit of each additional unit of resource
Can be obtained by examining the Zj row of primal optimal simplex table
Can be obtained by examining Cj-Zj row of primal optimal simplex table
All of the above
Sensitivity analysis
Is also called post-optimality analysis as it is carried out after the optimal solution is obtained
Allows the decision – maker more meaningful in formation about changes in the LP model parameters
Provides the range within which a parameter may change without affecting optimality
All of the above
When an additional variable is added in the LP model, the existing optimal solution can further be improved if
Cj-Zj = 0
Cj-Zj = 0
Both 1 and 2
None of the above
Addition of an additional constraint in the existing constraints will cause a
Change in objective function coefficients (Cj)
Change in coefficients aij
Both 1 and 2
One of the above
If an additional constraint added is an equation and an artificial variable appears in the basis of the new problem, the new optimal solution is obtained by
Assigning zero cost coefficient to the artificial variable if it appears in the basis at negative value
Assigning – M cost coefficient to the artificial variable if it appears in the basis at positive value
Either 1 and 2
None of the above
To ensure best marginal increase in the objective function value, a resource value may be increased whose shadow price is comparatively
Larger
Smaller
Neither 1 nor 2
Both 1 and 2