A model predictive control (MPC) module performs multiple iterations to determine a current set of target values for an engine based on a torque request, a model of the engine, a tableau matrix, and a basic solution matrix. Each of the iterations includes: determining whether the basic solution matrix is not in standard form; when the basic solution matrix is not in standard form, identifying a first column of the tableau matrix based on a first entry position of the primal variable of the non-basic pair; when the basic solution matrix is in standard form and one or more primal variables of the basic solution matrix are negative, identifying the first column of the tableau matrix based on a second entry position of a dual variable of the basic pair; and selectively updating the basic solution matrix based on the first column of the tableau matrix.