You are considering purchasing a firm that has three possible scenarios on how things play out.

First, the worst$-$case scenario has a probability of $40\%,$ and the company is worth $$100$ million. The base$-$case scenario has a $50\%$ chance of happening, and the company is worth $$150$ million. The best$-$case scenario has a $10\%$ probability, and the company is worth $$800$ million.

What is the highest amount you would be ready to pay for the company?

$($Enter your answer in millions. So$,$ if your answer is $$2\mathrm{.}5$ million, enter $"2\mathrm{.}5")$