I constructed the likelihood function: L(x|θ1,θ2) = (1/θ1)^n*exp(∑(i=1 to n)((-xi-θ2)/θ1) and the log likelihood: -n*log(θ1)+∑((-xi-θ2)/θ1) under H0, θ1 = θ1, to find θ2, I set the derivative of l(x|θ1,θ2) = 0 with respect to θ2, but since the derivative doesn't yield to a solution, I realized that the maximizer for the likelihood function is the x(1), which is the minimum of xi, so θhat2 = x(1). Under Ha, I set the derivative of l(x|θ1,θ2) = 0 with respect to θ1, and found that θhat1 = (∑(xi+θ2))/n. But when I construct the likelihood ratio, things get so complicated and I can't follow. Can anyone suggest a way to tackle this part of the problem?