In Exercises 1-6 use the simplex method to maximize the functions under the given constraints. Determine the basic and nonbasic variables and the entering variables and departing variables for each tableau. Determine the optimal solution and the maximum value of the objective function directly from the final tableau. (These problems were given in the previous set of exercises.Use the tableaux that you have already derived, and check your previous answers.) Maximize f = 2x + 4y + z subject to-x + 2y + 3z ::;; 6-x + 4y + Sz ::5 S-x + Sy + 7 z ::;; 7x ;::::: 0, y ;::::: 0, z ;::::: 0, w ;::::: 0(Exercise 7, Section 8.2)

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