You have just bought a run$-$down house in a historic presentationdistrict for $$220,000.$ You plan to renovate it$,$ after which youbelieve you can sell it for $$450,000.$ There are two different waysyou can perform the renovation, Plan A and Plan B$.$ Plan A wouldcost $$125,000$ and take three months. Plan B would cost $$85,000$ andtake four months; however, Plan B requires approval by the historicpreservation board. It will take the board two months to consider theproposal for Plan B and you believe the chance of the proposal beingapproved are $70\%.$ Each month you hold the property costs you $$1,500$in financing costs and property taxes. You are considering threeoptions: