Review set
Bases, Basic Solutions and Reduced Costs
Construct the point a basis determines, decide whether it is feasible, and price the nonbasic columns. The two competences are drilled together because the common failure is to run the optimality test on a basic solution that is not feasible, where the verdict means nothing.
What this involves
Retrieval after a delay, which is what makes knowledge durable.
Answers here count towards what the system knows about your skills.
What this covers
- Construct a basic solution from a chosen basis
Given a standard-form constraint system and a proposed set of columns, the learner can decide whether the set is a basis, construct the corresponding basic solution by setting nonbasic variables to zero and solving the square system, and state separately whether the result is feasible.
- Compute reduced costs and apply the optimality test
Given a minimization program in standard form and a specified basis, the learner can compute the reduced cost of each nonbasic variable and determine whether the corresponding basic feasible solution is optimal, without a formula sheet.
- Put a program in canonical form for a given basis
Given a standard-form program and a basis, the learner can partition the columns, solve for the basic variables, express the objective in the nonbasic variables alone, and read the basic solution, the objective value and the reduced costs off the result, stating whether the basis is optimal and why.