Three project crews are awarded a contract to construct an automated plant. The crews can work simultaneously on the project if necessary. Crew 1, working alone, can complete the project in 82 days. Crew 2, working alone, can complete the project in 50 days. Crew 3, working alone, can complete the project in 64 days. Crew 2 started the project. Ten days after the project started, crew 1 joined the project. Fifteen days after crew 1 joined the project, crew 3 also joined the project. Crew 2 left the project 5 days before it was completed. Crew 1 is paid \(\$ 500,000 /\) day on the project. Crew 2 is paid \(\$ 750,000 /\) day. Crew 3 is paid \(\$ 425,975 /\) day.

a. Find how many days it took to complete the project (assume that fractions of a day are permissible).

b. Based on the project participation described earlier, find the minimum budget needed to complete the project.