Let U1 = 8x-.5x^2 tx1 and U2 = 5x -.5x^2 tx2, where x = min{x1, x2}. x is a public good and its level is equal to the lowest contribution among agents 1 and 2. x1 is the amount of good x produced by agent 1 and x2 is the amount of good x produced by agent 2. t is the cost of an additional unit of x. let t=3

What are the social-optimal levels of x1 and x2? What is the optimal amount of x1 agent 1 would choose given x2?