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add row alive at age amount augmented matrix axis basic feasible solution Bayes Cartesian product coefficient compounded Computing consider the equation constraints convex set coordinates corner points corresponding defined denoted departing variable dual problem elementary event entering variable equal equation gives equivalent Exercise 11 Exercise 9 Exercise set explicit variables feasible region finite follows Gauss-Jordan elimination genotype AA graph Hence initial tableau integer interest formula labeled lies below line linear programming problem linear system matrix game Multiply row mutually exclusive events negative entries nonnegative number of units number tossed objective function obtain occurs optimal solution outcomes pair path probabilities payment payoff matrix player primal problem probability model random variable ratio Results to remember riboflavin row echelon form sample space second equation second row sequence slack variables slope solve the system standard normal curve system of equations third row total number Writing the objective