 # 3-7 For each of the following combinations of objective function, ...

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3-7 For each of the following combinations of objective function, point. and direction, deter- mine whether conditions 3.21 and 3.22 show that the direction improves at the point, does not improve at the point, or that further information is required. (b) max yi + 7y3 + 2ys, y = (1,0,9,0,0), Ay = (-10,-20,2,0,4) - (d) min y1y2 + 4y1 +(y2)²,y=(2,1), = Ay=(-1,3) = (f) min (y1 - 2² + y1y2 + (y2 - 3)², y = (1,1), Ay = (3,-1) 3-9 Determine which of the constraints (z1 - + (z2 - 1)2 s 25 [i] 2z1 - Z2 = 8 [ii] [iii] [iv] are active at each of the following solutions. (b) z = (6,4) = 3-10 Determine whether each of the directions specified is feasible at the solution indicated to the linear constraints 3y1 - 2y2 + 8y3 = 14 6y1 - 4y2 - 1y3 s 11 y1,y2,y3 > 0 (b) Ay = (0,-4,1)aty=(2,0,1 = (d) Ay = (-2,1,1) aty = (0, 1,2)

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