$$BIDA Thrive$$ is a college located in the West coast of Scotland. It has recently been awarded funding by the Scottish Government to build a department on the newly developed campus site, $2$ miles away from its existing location. This funding will only cover part of the total cost to build and run the new department over the next $10$ years. The remainder of the cost will be funded by other investors.

The college needs to choose a heating system for the new department and is considering the following choices: a traditional boiler system, solar powered panels or a wind operated system.

If the college chooses to use a traditional boiler system, there will be a capital cost of $45,000.$ In addition to this, the estimated annual heating cost will be $8,000.$

If the college chooses to install solar powered panels, there will be a capital cost of $70,000.$ This covers the cost of both the solar powered panels and a $$back$-$up$$ heating system for use when the solar powered panels are unable to provide enough energy. The annual cost of using the solar powered panels will be $900.$

There is a $70\%$ probability that the solar powered panels will be able to provide all the heating required throughout the year due to sufficient hours of sunshine. However, if the solar powered panels cannot provide all of the energy required, the $$back$-$up$$ system will be used and will cost an additional $4,000$ per year.

If $$BIDA Thrive$$ chooses to install a wind operated system, there will be a capital cost of $80,000.$ Due to the location of the college, there will be sufficient wind to power the heating from this system without the need for any $$back$-$up$$ system. The annual cost of the heating from this system will be $500.$

However, the college has been told that there will be an additional annual cost of maintenance for the wind powered system. The system will have either a low, medium or high number of faults and thus the maintenance cost will differ for each of these situations. There is a $40\%$ probability that the system will have a low number of faults with an annual maintenance cost of $1,000.$ There is a $35\%$ probability that the system will have a medium number of faults, resulting in an annual maintenance cost of $2,500.$ A high number of faults will result in an annual cost of $6,000.$

$1.$ What should $$BIDA Thrive$$ do$,$ based on the option that minimises the expected cost over the next $10$ years?

a$.$ to choose a traditional boiler

b$.$ to choose a solar system

c$.$ to either choose a solar system or a wind powered system

d$.$ to choose a wind powered system

$2.$ What is the expected value associated with the most beneficial course of action?

a$.91,000$

b$.112,570$

c$.79,000$

d$.95,000$

e$.87,750$