Warner Corporation purchased a machine $7$ years ago for $$350,000$ when it launched product P$50.$ Unfortunately, this machine has broken down and cannot be repaired. The machine could be replaced by a new model $300$ machine costing $$342,450$ or by a new model $200$ machine costing $$290,800.$ Management has decided to buy the model $200$ machine. It has less capacity than the model $300$ machine, but its capacity is sufficient to continue making product P$50.$ Management also considered, but rejected, the alternative of dropping product P$50$ and not replacing the old machine. If that were done, the $$290,800$ invested in the new machine could instead have been invested in a project that would have returned a total of $$400,400.$ Required: $1.$ What is the total differential cost regarding the decision to buy the model $200$ machine rather than the model $300$ machine? $2.$ What is the total sunk cost regarding the decision to buy the model $200$ machine rather than the model $300$ machine? $3.$ What is the total opportunity cost regarding the decision to invest in the model $200$ machine?