Richard Wilson, president of Sheridan Always, agrees to construct a concrete cart path at Sunny Golf Club. Sheridan Always enters into a contract with Sunny to construct the path for $$224,000.$ In addition, as part of the contract, a performance bonus of $$47,600$ will be paid based on the timing of completion. The performance bonus will be paid fully if completed by the agreed$-$upon date. The performance bonus decreases by $$11,900$ per week for every week beyond the agreed$-$upon completion date. Richard has been that he will receive a good portion of the performance bonus. Richard estimates, given the constraints of his schedule related to other jobs, that there is $60\%$ probability that he will complete the project on time, a $30\%$ probability that he will be $1$ week late, and a $10\%$ probability that he will be $2$ weeks late.