Part A

Consider the convex set given by 2 :1 + 612 20 4x1 + 2 12 2 12 T1 2 0, 12 20 (a) Introduce a slack variable , > 0 to convert the first inequality to an equation. The way to write z, in Mobius is x[1] (b) Introduce a slack variable x 2 0 to convert the second inequality to an equation. (c) Enter the 2x5 augmented matrix that comes from your answers to (a) and (b), with pivots in the third and fourth columns To enter a matrix click on the 3x3 grid of squares below. Next select the exact size of the matrix you want. Then change the entries in the matrix to the entries of your answer. If you need to start over then click on the trash can. sin (a) ? (d) Find a basic solution that is not feasible. It should have four components, for $1, $2, 13, $4 (e) Find a feasible basic solution. It should have four components, for $1 , 12, 13 , $4.Consider the region given by z E 2. 2 z + y 2 9, z+y 25 7. :,y,22 D {a} Formulate the problem using slack variables .91 2 D, 32 2 0 and 33 2 0. Write down the basic solution obtained by choosing the slack variables as pivots. Enter in the form (3,9,2, 31,52,531 | |li {b} Is this a feasible solution? O True False to] Write down the basic solution obtained by choosing 2,51,32 as pivots. Enter in the four: (2,35 z, 51,32,53) to} Is this a feasible solution? O True False (e1Write down the basic solution obtained by choosing z,y, 7. as pivots. Enter in the form (z,y,z,31,32,s3] (i) Is this a feasible solution? True 0 False