Peabody Construction Company enters into a contract with a customer to build a warehouse for $$100,000,$ with a performance bonus of $$50,000$ that will be paid based on the timing of completion. The amount of the performance bonus decreases by $10\%$ per week for every week beyond the agreed$-$upon completion date. The contract requirements are similar to contracts that Peabody has performed previously, and management believes that such experience is predictive for this contract. Management estimates that there is a $60\%$ probability that the contract will be completed by the agreed$-$upon completion date, a $30\%$ probability that it will be completed $1$ week late, and only a $10\%$ probability that it will be completed $2$ weeks late.