Find the dual of the following LP:

M a x space z equals 4 x subscript 1 minus x subscript 2 plus 2 x subscript 3

s. t.

x subscript 1 plus x subscript 2 less or equal than 5

2 x subscript 1 plus x subscript 2 less or equal than 7

2 x subscript 2 plus x subscript 3 greater or equal than 6

x subscript 1 plus x subscript 3 equals 4

x subscript 1 greater or equal than 0 comma space x subscript 2 space a n d space x subscript 3 space u r s

Select one:

a.

M i n space w equals 5 y subscript 1 plus 7 y subscript 2 plus 6 y subscript 3 plus 4 y subscript 4

s. t.

y subscript 1 plus 2 y subscript 2 plus y subscript 4 greater or equal than 4

y subscript 1 plus y subscript 2 plus 2 y subscript 3 equals 1

y subscript 3 plus y subscript 4 equals 2

y subscript 1 space comma y subscript 2 greater or equal than 0 comma space y subscript 3 less or equal than 0 comma space y subscript 4 space u r s

b.

M i n space w equals 5 y subscript 1 plus 7 y subscript 2 plus 6 y subscript 3 plus 4 y subscript 4

s. t.

y subscript 1 plus 2 y subscript 2 plus y subscript 4 greater or equal than 4

y subscript 1 plus y subscript 2 plus 2 y subscript 3 equals negative 1

y subscript 3 plus y subscript 4 equals 2

y subscript 1 space comma y subscript 2 greater or equal than 0 comma space y subscript 3 less or equal than 0 comma space y subscript 4 space u r s

c.

M i n space w equals 5 y subscript 1 plus 7 y subscript 2 plus 6 y subscript 3 plus 4 y subscript 4

s. t.

y subscript 1 plus 2 y subscript 2 plus y subscript 4 greater or equal than 4

y subscript 1 plus y subscript 2 plus 2 y subscript 3 equals negative 1

y subscript 3 plus y subscript 4 equals negative 2

y subscript 1 space comma y subscript 2 greater or equal than 0 comma space y subscript 3 less or equal than 0 comma space y subscript 4 space u r s

d.

M i n space w equals 5 y subscript 1 plus 7 y subscript 2 plus 6 y subscript 3 plus 4 y subscript 4

s. t.

y subscript 1 plus 2 y subscript 2 plus y subscript 4 less or equal than 4

y subscript 1 plus y subscript 2 plus 2 y subscript 3 equals negative 1

y subscript 3 plus y subscript 4 equals 2

y subscript 1 space comma y subscript 2 greater or equal than 0 comma space y subscript 3 less or equal than 0 comma space y subscript 4 space u r s