$-\mathrm{.}21$ Ronald Lau, chief engineer at South Dakota

Electronics, has to decide whether to build a new state$-$of$-$the$-$art

processing facility. If the new facility works, the company could

realize a profit of $$200,000.$ If it fails, South Dakota Electronics

could lose $$180,000.$ At this time, Lau estimates a $60\%$ chance

that the new process will fail.

The other option is to build a pilot plant and then decide

whether to build a complete facility. The pilot plant would cost

$$10,000$ to build. Lau estimates a $50-50$ chance that the pilot plant

will work. If the pilot plant works, there is a $90\%$ probability that

the complete plant, if it is built, will also work. If the pilot plant

does not work, there is only a $20\%$ chance that the complete pro$-$

ject $($if it is constructed$)$ will work. Lau faces a dilemm Should he

build the plant? Should he build the pilot project and then make a

decision? Help Lau by analyzing this problem.