Question

When can multiple optimal solutions can occur in linear programming problems? Explain.

Answer 1

Linear programming issues comprise of target capacities utilizing certain choice factors and an arrangement of requirements that should be clung to. In a perfect world, a linear programming issue has an interesting ideal arrangement (set of choice factors).

Not withstanding, there are circumstances when there are interchange arrangements that fulfill the limitations and furthermore the goal work. In such case, the linear writing computer programs is said to have an ideal arrangement.

One of the most effortless approach to recognize whether a straight programming has numerous ideal arrangement is to decide the imperatives first. On the off chance that the coupling limitation has indistinguishable incline from the goal work, at that point there will be different substitute arrangements. A coupling limitation is a requirement that is fulfilled totally in the ideal arrangement. There are not slacks or surplus with a coupling requirement. Along these lines if such imperative has a similar slant (or keeps running in parallel) as the target work at that point there will be numerous ideal arrangement. This outcomes in weighted normal of fundamental ideal arrangements in yielding an option non-essential plausible arrangement.

Consider the issue demonstrated as follows

Expand Z, where

Z = 3x + 2Y

Subject to limitations

x <= 40

y <= 60

3x + 2y <= 180

x,y >= 0

Essentially a certifiable case of various ideal arrangements could be distinctive item blends where the extents of the blend isn't a limitation. In such cases, there could be different arrangements that give same and the most extreme income alternative or least cost choice.