You're talking about Book 1? I thought since we were discussing the Red Wedding we were discussing Book 3 at minimum.
Yes of course in Book 1, it's not public knowledge that Joffrey is a bastard. That changes at the start of season 2 when Stannis sends everyone a raven saying "my brother got cucked T_T". As soon as that letter is sent, it's common knowledge among all the lords and ladies that Joffrey is a bastard. Just like it's common knowledge among the lords and ladies that Tywin was part of the Red Wedding.
So if Tywin cared about saving man power, provisions, money, and resources, then why did he start a war that he didn't need to start in the first place during Book 1?
You can't paint Mr. Starts Wars for No Good Reason as someone who cares about saving man power and resources.
Also as I said in my previous post, all those are short term gains with long term consequences. With the Tyrells carrying Tywin on his back, he doesn't need to worry about money, food, or man power. Tyrells have all of that and more. Tyrells got the largest army and the most food. What resources does Tywin need to worry about with the Tyrells at his side?
The Red Wedding was silly no matter what angle you try looking at it from. It ruined House Lannister and House Frey's reputation. I'll say it again, it had very short term gains with very long term consequences. If the author ever decides to continue the books, I promise you'll continue to see people in the books showing disgust at the Freys and Lannisters over the Red Wedding.