A large machine in a factory has broken down and the company that owns the factory will incurcosts of $$3000$ for every day the machine is out of service. The factory$$s engineer has three imme$-$diate optionsA large machine in a factory has broken down and the company that owns the factory will incur

costs of $$3000$ for every day the machine is out of service. The factory's engineer has three imme$-$

diate options:

Option $1$: She can return the machine to the supplier who has agreed to collect, repair, and return

it free of charge, but not to compensate the company for any losses they might incur while the

repair is being carried out. The supplier will not agree to repair the machine if any other person

has previously attempted to repair it$.$ If the machine is returned, the supplier will guarantee to

return it in working order in $10$ days' time.

Option $2$: She can call in a specialist local engineering company. They will charge $$20,000$ to carry

out the repair, and they estimate that there is a $30\%$ chance that they will be able to return the

machine to working order in $2$ days. There is$,$ however, a $70\%$ chance that repairs will take $4$ days.

Option $3$: She can attempt carry out the repair work herself, and she estimates that there is a $50\%$

chance that she could mend the machine in $5$ days. However, if at the end of $5$ days the attempted

repair has not been successful, she will then have to decide whether to call in the local engineering

company or to make a second attempt at repair by investigating a different part of the mechanism.

This would take two further days, and she estimates that there is a $25\%$ chance that this second

attempt would be successful. If she fails at the second attempt, she will have no alternative other

than to call in the local engineering company.

Please do the following:

Draw a decision tree to represent this problem.

Calculate the total value at each endpoint.

Solve the decision tree and summarize the optimal decision strategy

Suppose that the engineer is unsure of her estimate of there being a $50\%$ chance that she

could fix the machine herself in $5$ days. Conduct a sensitivity analysis on that estimate. What

does the result of that analysis tell you?