a. Solve the following (knapsack) problem. b. Maximize 2x + 3x2 + 8x3 + X4 +...

 

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a. Solve the following (knapsack) problem. b. Maximize 2x₁ + 3x2 + 8x3 + X4 + 5x5 subject to 3x1 + 5x2 + 11x3 + 2x4 + 7x5 ≤ 10 X1, X2, X3, X4, X5 ≥ 0. Give a generalized closed-form solution for the following problem in terms of the ratios c¡/aj, j = 1, ..., n: Maximize C₁x tt Chăn subject to a₁x1 ++ Anxn b X1, xn ≥ 0, where c; and a; are positive scalars for each j. C. What is the form of the optimal solution if and be any scalars in Part (b)? cj aj are allowed to d. Extend Parts (b) and (c) to include upper bounds on the variables. a. Solve the following (knapsack) problem. b. Maximize 2x₁ + 3x2 + 8x3 + X4 + 5x5 subject to 3x1 + 5x2 + 11x3 + 2x4 + 7x5 ≤ 10 X1, X2, X3, X4, X5 ≥ 0. Give a generalized closed-form solution for the following problem in terms of the ratios c¡/aj, j = 1, ..., n: Maximize C₁x tt Chăn subject to a₁x1 ++ Anxn b X1, xn ≥ 0, where c; and a; are positive scalars for each j. C. What is the form of the optimal solution if and be any scalars in Part (b)? cj aj are allowed to d. Extend Parts (b) and (c) to include upper bounds on the variables. a. Solve the following (knapsack) problem. b. Maximize 2x₁ + 3x2 + 8x3 + X4 + 5x5 subject to 3x1 + 5x2 + 11x3 + 2x4 + 7x5 ≤ 10 X1, X2, X3, X4, X5 ≥ 0. Give a generalized closed-form solution for the following problem in terms of the ratios c¡/aj, j = 1, ..., n: Maximize C₁x tt Chăn subject to a₁x1 ++ Anxn b X1, xn ≥ 0, where c; and a; are positive scalars for each j. C. What is the form of the optimal solution if and be any scalars in Part (b)? cj aj are allowed to d. Extend Parts (b) and (c) to include upper bounds on the variables. a. Solve the following (knapsack) problem. b. Maximize 2x₁ + 3x2 + 8x3 + X4 + 5x5 subject to 3x1 + 5x2 + 11x3 + 2x4 + 7x5 ≤ 10 X1, X2, X3, X4, X5 ≥ 0. Give a generalized closed-form solution for the following problem in terms of the ratios c¡/aj, j = 1, ..., n: Maximize C₁x tt Chăn subject to a₁x1 ++ Anxn b X1, xn ≥ 0, where c; and a; are positive scalars for each j. C. What is the form of the optimal solution if and be any scalars in Part (b)? cj aj are allowed to d. Extend Parts (b) and (c) to include upper bounds on the variables.