(Solution) - Reconsider the integer nonlinear programming model given in Prob 11 3 9 a -(2025 Original AI-Free Solution)

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Reconsider the integer nonlinear programming model given in Prob. 11.3-9.
(a) Show that the objective function is not concave.
(b) Formulate an equivalent pure binary integer linear programming model for this problem as follows. Apply the separable programming technique with the feasible integers as the breakpoints of the piecewise linear functions, so that the auxiliary variables are binary variables. Then add some linear programming constraints on these binary variables to enforce the special restriction of separable programming. (Note that the key property of separable programming does not hold for this problem because the objective function is not concave.)