You are tasked with selecting a solar array for the next generation of communication satellites

that your company is developing. You have three options: Material A$,$ Material B$,$ and Material

C$.$ Your engineering team really likes Material A because it achieves a $45\%$ efficiency in

converting sunlight to electrical power. They prefer to not use Material C because it is

considered dated in the solar power community. Material B seems a good compromise between

the two, with a $30\%$ efficiency.

The sales department estimates that the $45\%$ efficiency can lead to sales between $$600M$ and

$$800M($with $60$:$40$ odds$).$ Material B can perform decently in the market, leading to sales

between $$400M$ and $$700M($with $80$:$20$ odds$).$ Material C may still generate revenue in the

order of $$500M.$ They are $50\%$ confidence about this, since a competitor may also launch a

better product, in which case sales with Material $C$ would be $$0.$

The cost to develop solar arrays with Material A is estimated at somewhat between $$100M$

$($with $50\%$ confidence$)$ and $$300M($with $50\%$ confidence$).$ The cost to develop solar arrays

with Material B is estimated at $$85M$ with a $10\%$ risk of overrunning to $$120M.$ The cost to

develop solar arrays with Material C is estimated at $$50M,$ which includes $$30M$ of raw material

that you already have in stock and cannot be resold.

Material A is a new development and, after talking to the subject matter experts, you realize

that there is a $35\%$ chance the development is too late to meet the time to market, which

would reduce your sales by $60\%.$ However, if the development is late, you can quickly react

and manufacture the solar arrays with Material $C$ to meet the time to market without any cost

impact, given that you already have all the material in stock.

With the objective of maximizing profit, choose what material to use for developing and

manufacturing the solar arrays.