Chapter 6.3, Problem 4P

Explanation of Solution

New optimal solution

• Let ${\text{x}}_{\text{1}}$ be the number of desks produced, ${\text{x}}_{\text{2}}$ be the number of tables produced and ${\text{x}}_{\text{3}}$ be the number of chairs produced.
• Let ${\text{c}}_{\text{i}}$ be the right hand side of the optimal table’s constraints.
• For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
• For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price).
• If the table is sold for $50 and one board feet of lumber, three finishing hours and 1.5 carpentry hours are used, and then the current basis will no longer be optimal.
• The new optimal table is determined by computing the columns in the current optimal table