need help with a,c and e Consider the region given by x S 8, -2x +yz7 x,y,z 0 a)

Question

need help with a,c and e

Consider the region given by x S 8, -2x +yz7 x,y,z 0 a) Formulate the problem using form (x, y, z, S1,82,83) slack variables s1 20, s2 20 and s3 2 0. Write down the basic solution obtained by choosing the slack variables as pivots. Enter in the (b) Is this a feasible solution True False o) Wirite down the basic solution obtained by choosing 2, 51,2 as pivots. Enter in the form (x,y,2,1,2,3. (d) Is this a feasible solution True False e) Write down the basic solution obtained by choosing x, y, z as pivots. Enter in the form (xy, z, S1, 82,$3 (f) Is this a feasible solution True O False

Explanation / Answer

x+s1 = 8

2x-y+s2 = -7

x+2y-z+s3 = 2

(a) slacks as pivot

x = 0 , y = 0 , z = 0 ,

s1 = 8

s2 = -7

s3 = 2

(0,0,0,8,-7,2)

(c)

x+s1 = 8

2x-y+s2 = -7

x+2y-z+s3 = 2

z , s1 , s2 pivots

x = 0 , y = 0 ,s3 = 0

s1 = 8

s2 = -7

z = -2

(0,0,-2,8,-7,0)

(e)

x+s1 = 8

2x-y+s2 = -7

x+2y-z+s3 = 2

s1 = 0 , s2 = 0 , s3 = 0

x = 8

y = 23

z = 8+2*23 - 2 = 52

(8,23,52,0,0,0)

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