Donald Robinson, president of Ivanhoe Always, agrees to construct a concrete cart path at Kingbird Golf Club. Ivanhoe Always enters into a contract with Kingbird to construct the path for $$181,000.$ In addition, as part of the contract, a performance bonus of $$39,600$ 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 $$9,900$ per week for every week beyond the agreed$-$upon completion date. Donald has been involved in a number of contracts that had performance bonuses as part of the agreement in the past. As a result, he is fairly confident that he will receive a good portion of the performance bonus. Donald 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 $25\%$ probability that he will be $1$ week late, and a $15\%$ probability that he will be $2$ weeks late.

$($a$)$

Determine the transaction price that Ivanhoe Always should compute for this agreement.

Transaction price $