Alternatives and Scope

Compare Alternatives

A cover is not just cheap; it must leave no demand point missing.

highlighted = computed this step

Chosen cover

A plus B plus C is feasible with cost 9.

chosen cost=9\text{chosen cost}=9
Visible alternativesAlternatives are checked by the same coverage and cost arithmetic.alternative checkscostmissingfeasibleA plus B plus C901B plus D1001A plus C510

B plus D

B plus D also covers all points, but its cost is 10.

cost(B+D)=10\text{cost}(B+D)=10
B plus DB plus D covers all points but costs more than the chosen cover.B plus D covers all pointschosen cost 10chosen rows B+Dpoint 1point 2point 3point 4point 5Acost 3cancan---Bcost 4-covercovercover-Ccost 2---cancanDcost 6cover---covercoveredcoveredcoveredcoveredcoveredfeasible cover

A plus C

A plus C costs only 5, but it leaves 1 demand point missing.

missing under A+C=1\text{missing under }A+C=1
A plus CA plus C is cheaper but leaves point three uncovered.A plus C misses point threechosen cost 5chosen rows A+Cpoint 1point 2point 3point 4point 5Acost 3covercover---Bcost 4-cancancan-Ccost 2---covercoverDcost 6can---cancoveredcoveredmissingcoveredcoveredmissing demand

Best visible cover

The exact enumeration checks every small subset and confirms the minimum feasible cost is 9.

min⁡ feasible cost=9\min\text{ feasible cost}=9
Visible alternativesAlternatives are checked by the same coverage and cost arithmetic.alternative checkscostmissingfeasibleA plus B plus C901B plus D1001A plus C510