Machines, items and time in a combined proportion

The time \(t\) hours that \(n\) identical machines take to produce \(N\) items is directly proportional to \(N\) and inversely proportional to \(n\). Four machines produce \(600\) items in \(5\) hours.

1. Find the time taken by \(9\) machines to produce \(1350\) items.[2]
2. The number of machines is increased by \(25\%\) and the number of items is increased by \(50\%\). Find the percentage change in the time taken.[3]
3. Find the least number of machines needed to produce \(2000\) items in less than \(6\) hours.[3]
4. In a later run, \(10\) machines produce \(1800\) items in \(5.5\) hours. Use the quantity \(\dfrac{tn}{N}\) to decide whether this run fits the model, and suggest a reason for any difference.[2]