Your friend Tenfour Goodbuddy is an independent trucker whose truck is empty after his most recent job. He has found a deal to take a load to Birmingham, with a return load included, for a total of $$3000.$ Another deal would give him a load to Charlotte for $$2500,$ with no guarantee of a return load. Tenfour thinks there's a $50\%$ chance of finding a $$2500$ return load from Charlotte.Otherwise, he must return empty with no revenue. Assume that the cost of a round trip to either city is the same, and that he sees no other loads presently available.a$)[5]$ Suppose Tenfour can obtain perfect information on the existence of a return load from Charlotte. What is the value of this information? Answer without drawing a decision tree!b$)[10]$ Ignore part $($a$)$ and suppose now that before deciding which deal to take, Tenfour can call his friend at the truck stop in Charlotte. Tenfour believes his friend will respond either by saying "It's Busy" $($with a $55\%$ probability$),$ in which case there is a $9/11$ chance that there will be a return load from Charlotte; or$,$ by saying "It's Slow" $($with a $45\%$ probability$),$ in which case there is a $8/9$ chance that there will be no return load. Neatly draw the decision tree that includes all decisions and chance events, as well as all payoffs and probabilities!c$)[8]$ Solve the decision tree in part $($b$),$ state the resulting optimal decision strategy that maximizes Tenfour's expected payoff, and state the expected value of that strategy.