As an example, suppose that t_0 = 1 in the 95% confidence interval example above.
Using the spreadsheet to solve (3) gives θ_L^* = 0, θ_H^* = .2161, λ_1^* = 0, λ_2^* = 18.4961, and λ_3^* = .9748 (the values of the Lagrange multipliers were obtained from the sensitivity report available in the software), which results in p_1 = .05 and p_2 = 0 and satisfies the optimality conditions in (7).