Q$.2$ A construction company has obtained a contract for a highway project and will need to lease an additional road grader for a month to fill out its equipment fleet. The company is trying to decide between two different lease options for the grader: $1)$ lease an older grader for $\backslash (\backslash$$ $8,500\backslash ),$ or $2)$ lease a newer grader for $\backslash (\backslash$$ $10,000\backslash ).$ The newer grader is still under warranty, so the lease cost covers all repair expenses. However, the company would be responsible for any repair expenses if it leases the older grader. The construction company's maintenance foreman believes there is a $\backslash (30\backslash \%\backslash )$ chance that there will be no need for repairs with the older grader, but also thinks there is a $\backslash (45\backslash \%\backslash )$ chance that some repairs $\backslash ((\backslash$$ $2,000\backslash ))$ could be needed, and a $\backslash (25\backslash \%\backslash )$ chance that significant repairs $\backslash ((\backslash$$ $5,000)\backslash )$ might be required. $($A$)$ Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. $($B$)$ What is the best lease option? Why? $($C$)$ Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision. If the mechanic is always correct in his assessments, what is the most the company would pay for the inspection?