Knowing what you now know about the material covered in Chap

Knowing what you now know about the material covered in Chapters 2 AND 3, please provide one example of a non-binding constraint as well as the \"slack\" that might be accompanied by it.

if at all possible, pick an example from home or your own place of business instead

Solution

¨Example

–Let X = the number of Tables made per week,

   Let Y = the number of Chairs made per week,

–

–Maximise Profit = 4X + 3Y   Objective Function

    Subject to

        4X+1Y <or = 90                      Wood

        2X+1Y <or = 50                      Machine-Time

        1X +1Y<or = 40                     Polishing-Time

        X, Y >or= 0

¨

¨Wood constraint

–4X + 1Y <or= 90

–Optimal Solution(X,Y)=(10,30),

–the wood used 4*10+1*30=70 kilograms

–20 kilograms unused---slack value   

–Let RHS 90 -> 90+1 or 90-1

–The optimal solution does not change.

–The addition or removing of one kilogram of Wood makes no difference to the optimal production plan. The Wood constraint is thus a Non-Binding constraint.

–Optimal Solution(X,Y)=(10,30),

–the wood used 4*10+1*30=70 kilograms

–20 kilograms unused---slack value   

–Let RHS 90 à 90+1 or 90-1

–The optimal solution does not change.

–The addition or removal of one kilogram of Wood makes no difference to the optimal production plan. The Wood constraint is said to be a Non-Binding constraint.