A machine needs to be immediately replaced in a certain manufacturing facility, as the machine downtime costs are $$2,000$ per hour. The supply manager looking to purchase a machine was evaluating two alternatives. Machine A Machine B Cost $$100,000$ $$125,000$ Delivery time $50$ days $45$ days Downtime costs $$2,000/$ hour $$2,000/$ hour a$)$ Calculate the lost revenue based on the delivery time difference and downtime costs, considering the machines will run $8$ hours a day and $7$ days a week. b$)$ Based on your results, what is the best alternative and why? Explain quantitatively. c$)$ Consider now a different scenario. You have acquired Machine B$.$ Your demand forecast has been stable until your sale price suddenly increased from $$10,000$ to $$11,000$ per day. i$)$ Considering you have acquired machine B$,$ what would be the daily lost revenue in sales during a $15-$day period? ii$)$ Considering lost sales in a $15-$day period against lost revenues based on the delivery time $($question a$),$ would you still have acquired machine B$?$ Why?