Gary - a The feasible region is bounded by line segments...

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The feasible region is bounded by line segments that consecutively connect extreme points (0, 0), (0, 4), (3, 5), (8, 0) and (0, 0). [Note that (0, 0) is listed twice to "finish the circuit."] SAME AS PREVIOUS EMAIL b (0, 0): s1 and s2 are basic, x1 and x2 are nonbasic. (0, 4): x2 and s2 are basic, x1 and s1 are nonbasic. (3, 5): x1 and x2 are basic, s1 and s2 are nonbasic. (8, 0): x1 and s1 are basic, x2 and s2 are nonbasic. SAME AS FIRST WORKING OF #4. c The values that minimize z = -5x1 + x2 are the values that maximize y = 5x1 - x2. *** y = - z *** THIS TIME: use x1 and s1 for nonbasic variables 3x2 = 12 + x1 - s1 x2 + s2 = 8 - x1 y + x2 = -5x1 y x2 s2 [0 3 0 | 12 + x1 - s1] [0 1 1 | 8 - x1 ] [1 1 0 | -5x1 ] Replace R1 with (1/3)R1. [0 1 0 | 4 + (1/3)x1 - (1/3)s1] [0 1 1 | 8 - x1 ] [1 1 0 | -5x1 ] Replace R2 with R2 - R1. Replace R3 with R3 - R1. [0 1 0 | 4 + (1/3)x1 - (1/3)s1] [0 0 1 | 4 - (4/3)x1 + (1/3)s1] [1 0 0 | -4 - (16/3)x1 + (1/3)s1] y = -4 - (16/3)x1 + (1/3)s1 x2 = 4 + (1/3)x1 - (1/3)s1
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Gary - a The feasible region is bounded by line segments...

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