# Model tp099
param a_1 := 0;
param a_2 := 50;
param a_3 := 50;
param a_4 := 75;
param a_5 := 75;
param a_6 := 75;
param a_7 := 100;
param a_8 := 100;
param b := 32;
param t_1 := 0;
param t_2 := 25;
param t_3 := 50;
param t_4 := 100;
param t_5 := 150;
param t_6 := 200;
param t_7 := 290;
param t_8 := 380;
param s_1 := 0;
param q_1 := 0;
param r_1 := 0;
var x_1 >= 0, <= 1.58;
let x_1 := 0.5;
var x_2 >= 0, <= 1.58;
let x_2 := 0.5;
var x_3 >= 0, <= 1.58;
let x_3 := 0.5;
var x_4 >= 0, <= 1.58;
let x_4 := 0.5;
var x_5 >= 0, <= 1.58;
let x_5 := 0.5;
var x_6 >= 0, <= 1.58;
let x_6 := 0.5;
var x_7 >= 0, <= 1.58;
let x_7 := 0.5;
var s_2 = s_1 + (t_2 - t_1)*(a_2*sin(x_1) - b);
var s_3 = s_2 + (t_3 - t_2)*(a_3*sin(x_2) - b);
var s_4 = s_3 + (t_4 - t_3)*(a_4*sin(x_3) - b);
var s_5 = s_4 + (t_5 - t_4)*(a_5*sin(x_4) - b);
var s_6 = s_5 + (t_6 - t_5)*(a_6*sin(x_5) - b);
var s_7 = s_6 + (t_7 - t_6)*(a_7*sin(x_6) - b);
var s_8 = s_7 + (t_8 - t_7)*(a_8*sin(x_7) - b);
var q_2 = q_1 + 0.5*(t_2 - t_1)^2*(a_2*sin(x_1) - b) + (t_2 - t_1)*s_1;
var q_3 = q_2 + 0.5*(t_3 - t_2)^2*(a_3*sin(x_2) - b) + (t_3 - t_2)*s_2;
var q_4 = q_3 + 0.5*(t_4 - t_3)^2*(a_4*sin(x_3) - b) + (t_4 - t_3)*s_3;
var q_5 = q_4 + 0.5*(t_5 - t_4)^2*(a_5*sin(x_4) - b) + (t_5 - t_4)*s_4;
var q_6 = q_5 + 0.5*(t_6 - t_5)^2*(a_6*sin(x_5) - b) + (t_6 - t_5)*s_5;
var q_7 = q_6 + 0.5*(t_7 - t_6)^2*(a_7*sin(x_6) - b) + (t_7 - t_6)*s_6;
var q_8 = q_7 + 0.5*(t_8 - t_7)^2*(a_8*sin(x_7) - b) + (t_8 - t_7)*s_7;
var c_1 = q_8 - 100000;
var c_2 = s_8 - 1000;
var r_2 = r_1 + a_2*(t_2 - t_1)*cos(x_1);
var r_3 = r_2 + a_3*(t_3 - t_2)*cos(x_2);
var r_4 = r_3 + a_4*(t_4 - t_3)*cos(x_3);
var r_5 = r_4 + a_5*(t_5 - t_4)*cos(x_4);
var r_6 = r_5 + a_6*(t_6 - t_5)*cos(x_5);
var r_7 = r_6 + a_7*(t_7 - t_6)*cos(x_6);
var r_8 = r_7 + a_8*(t_8 - t_7)*cos(x_7);
var mf = -r_8^2;
minimize obj: mf;
subject to ce_1: c_1 = 0;
subject to ce_2: c_2 = 0;
display obj;
solve;
display obj;
display x_1;
display x_2;
display x_3;
display x_4;
display x_5;
display x_6;
display x_7;
display obj + 831079891.5101075;
display x_1 - 0.542467816212317;
display x_2 - 0.5290214242019767;
display x_3 - 0.5084491553164001;
display x_4 - 0.4802688509618159;
display x_5 - 0.4512363497966467;
display x_6 - 0.4091830824209853;
display x_7 - 0.3527878917811228;