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Allen Corp. enters into a contract with a customer to build an apartment building for $\backslash$$$1,031,300.$ The customer hopes to rent apartments at the beginning of the school year and provides a performance bonus of $\backslash (\backslash$$ $144,300\backslash )$ to be paid if the building is ready for rental beginning August $1,2026.$ The bonus is reduced by $\backslash (\backslash$$ $48,100\backslash )$ each week that completion is delayed. Allen commonly includes these completion bonuses in its contracts and, based on prior experience, estimates the following completion outcomes:

$($a$)$ Determine the transaction price for the contract, assuming Allen is only able to estimate whether the building can be completed by August $1,2026,$ or not $($Allen estimates that there is a $70\backslash \%$ chance that the building will be completed by August $1,2026).$

Transaction price $\backslash$$

$($b$)$ Determine the transaction price for the contract, assuming Allen has limited information with which to develop a reliable estimate of completion by the August $1,2026,$ deadline.

Transaction price