Steve Hinton, the owner of COM$-$TECH, a small communications research firm located just outside

of Raleigh, North Carolina, is trying to develop a design for using wireless communication

technology to enhance the safety of the coal$-$mining industry. Upon successful development of this

design, he would be able to sell it to the Occupational Safety and Health Administration $($OSHA$)$ at

a price of $$85,000.$

Steve would need to decide to use one of the three available communication technologies:

microwave, cellular, or infrared. He has some experience in all three areas but would need to

acquire some new equipment depending on which technology is used. The cost of equipment

needed for each technology is summarized as:

Technology Equipment Cost

Microwave $$4,000$

Cellular $$5,000$

Infrared $$4,000$

In addition to the equipment cost, Steve knows he will spend money on research and development

$($R&D$)$ to carry out the design development, but he does not know exactly what the R&D costs will

be$.$ For simplicity, Steve estimates the following best$-$case and worst$-$case R&D costs associated

with using each technology, and he assigns probabilities to each outcome based on his degree of

expertise in each area.

Possible R&D Costs

Best Case Worst Case

Cost Probability Cost Probability

Microwave $$30,0000\mathrm{.}4$ $$60,0000\mathrm{.}6$

Cellular $$40,0000\mathrm{.}8$ $$70,0000\mathrm{.}2$

Infrared $$40,0000\mathrm{.}9$ $$80,0000\mathrm{.}1$

Submit:

$1-$ What is the best course of decision for Steve in this problem?

$2-$ What is the expected profit for this best course of action?

$3-$ What is the expected value of perfect information? $($This part is optional and for extra credit$)$