4) min 4x1 + 3x2 + 6x3 s. t. x1 + 0.5x2 + x3 ≥ 15 2x2 + x3 ≥ 30 x1 + x2 + 2x3 ≥ 15 x1,x2,x3 ≥ 0 a) find the optimal solution by entering this problem into excel. b) run the sensitivity report and use it to find the optimal solution to the dual problem [do not solve the dual by using solver]. c) formulate the dual problem. d) verify that the strong duality theorem and all complementary slackness conditions (there are six of them) hold.

Determine the common ratio and find the next three terms of the geometric sequence. 649-14-02-00-00_files/i0100000, 649-14-02-00-00_files/i0100001, 2, a. 3; 649-14-02-00-00_files/i0100002, 649-14-02-00-00_files/i0100003, 649-14-02-00-00_files/i0100004. c. 649-14-02-00-00_files/i0100005; 649-14-02-00-00_files/i0100006, 649-14-02-00-00_files/i0100007, 649-14-02-00-00_files/i0100008. b. 3; 6, 18, 54 d. 649-14-02-00-00_files/i0100009. 6, 18, 54 select the best answer from the choices provided a b c d