x_{1} = \operatorname{piecewise}(200, \operatorname{or}\left(t < 2, t \ge 8\right), \operatorname{piecewise}(300, \operatorname{and}\left(t \ge 2, t < 5\right), \operatorname{piecewise}(100, \operatorname{and}\left(t \ge 5, t < 8\right), 200)))