The consultancy Imagination Inc. is working with its manufacturing client Parts$-$R$-$Us to improve their on$-$time performance. The firm can earn a bonus of up to $$1,000,000$ based on how much the on$-$time performance actually improves. It's current $($baseline$)$ on$-$time performance is $90\%.$

The company typically completes approximately $1,000$ orders per month, with approximately $100$ orders delayed. The bonus payment is prorated according to the following criteria:

The on$-$time performance improvement is calculated based on a reduction in late events or an improvement in on$-$time performance.

No bonus is earned for the first $25\%$ reduction in late events, say from $100$ to $75.$ Maximum bonus is earned once Parts$-$R$-$Us achieves $95\%$ on$-$time performance.

Please answer the following:

Write down a formula to determine the total bonus amount to be received

Using your formula, show how much bonus would be paid if Parts$-$R$-$Us achieves $94\%$ on$-$time performance.